Relevant bibliographies by topics / Mathematical optimization

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Mathematical optimization'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 June 2025

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Journal articles on the topic "Mathematical optimization"

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Kulcsár, T., and I. Timár. "Mathematical optimization and engineering applications." Mathematical Modeling and Computing 3, no. 1 (July 1, 2016): 59–78. http://dx.doi.org/10.23939/mmc2016.01.059.

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Bhardwaj, Suyash, Seema Kashyap, and Anju Shukla. "A Novel Approach For Optimization In Mathematical Calculations Using Vedic Mathematics Techniques." MATHEMATICAL JOURNAL OF INTERDISCIPLINARY SCIENCES 1, no. 1 (July 2, 2012): 23–34. http://dx.doi.org/10.15415/mjis.2012.11002.

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Chawla, Dr Meenu. "Mathematical optimization techniques." Pharma Innovation 8, no. 2 (January 1, 2019): 888–92. http://dx.doi.org/10.22271/tpi.2019.v8.i2n.25454.

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Suhl, Uwe H. "MOPS — Mathematical optimization system." European Journal of Operational Research 72, no. 2 (January 1994): 312–22. http://dx.doi.org/10.1016/0377-2217(94)90312-3.

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Blaydа, I. A. "OPTIMIZATION OF THE COAL BACTERIAL DESULFURIZATION USING MATHEMATICAL METHODS." Biotechnologia Acta 11, no. 6 (December 2018): 55–66. http://dx.doi.org/10.15407/biotech11.06.055.

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Requelme Ibáñez, Rosa María, Carlos Abel Reyes Alvarado, and Jorge Luis Lozano Cervera. "Mathematical optimization for economic agents." Revista Ciencia y Tecnología 17, no. 3 (September 9, 2021): 81–89. http://dx.doi.org/10.17268/rev.cyt.2021.03.07.

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Sezer, Ali Devin, and Gerhard-Wilhelm Weber. "Optimization Methods in Mathematical Finance." Optimization 62, no. 11 (November 2013): 1399–402. http://dx.doi.org/10.1080/02331934.2013.863528.

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Stanojević, Milan, and Bogdana Stanojević. "Lua APIs for mathematical optimization." Procedia Computer Science 242 (2024): 460–65. http://dx.doi.org/10.1016/j.procs.2024.08.160.

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García, J. M., C. A. Acosta, and M. J. Mesa. "Genetic algorithms for mathematical optimization." Journal of Physics: Conference Series 1448 (January 2020): 012020. http://dx.doi.org/10.1088/1742-6596/1448/1/012020.

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Gorissen, Bram L., Jan Unkelbach, and Thomas R. Bortfeld. "Mathematical Optimization of Treatment Schedules." International Journal of Radiation Oncology*Biology*Physics 96, no. 1 (September 2016): 6–8. http://dx.doi.org/10.1016/j.ijrobp.2016.04.012.

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Dissertations / Theses on the topic "Mathematical optimization"

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Keanius, Erik. "Mathematical Optimization in SVMs." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297492.

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In this thesis, support vector machines (SVMs) are studied from a mathematical optimization viewpoint. Both the linear case using hard-margin as well as soft-margin classification and the non-linear case using kernel functions are discussed. The theory of kernel Hilbert spaces is introduced and related to the non-linear SVM case. Moreover, fundamental theorems from optimization, including Lagrangian duality and KKT conditions, are introduced and proved. These theorems are then applied to the optimization problem of SVMs. Finally, the SVM optimization problem is implemented, solved, and visualized in Python.
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Zhou, Fangjun. "Nonmonotone methods in optimization and DC optimization of location problems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/21777.

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Holm, Åsa. "Mathematical Optimization of HDR Brachytherapy." Doctoral thesis, Linköpings universitet, Optimeringslära, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-99795.

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One out of eight deaths throughout the world is due to cancer. Developing new treatments and improving existing treatments is hence of major importance. In this thesis we have studied how mathematical optimization can be used to improve an existing treatment method: high-dose-rate (HDR) brachytherapy. HDR brachytherapy is a radiation modality used to treat tumours of for example the cervix, prostate, breasts, and skin. In HDR brachytherapy catheters are implanted into or close to the tumour volume. A radioactive source is moved through the catheters, and by adjusting where the catheters are placed, called catheter positioning, and how the source is moved through the catheters, called the dwelling time pattern, the dose distribution can be controlled. By constructing an individualized catheter positioning and dwelling time pattern, called dose plan, based on each patient's anatomy, it is possible to improve the treatment result. Mathematical optimization has during the last decade been used to aid in creating individualized dose plans. The dominating optimization model for this purpose is a linear penalty model. This model only considers the dwelling time pattern within already implanted catheters, and minimizes a weighted deviation from dose intervals prescribed by a physician. In this thesis we show that the distribution of the basic variables in the linear penalty model implies that only dwelling time patterns that have certain characteristics can be optimal. These characteristics cause troublesome inhomogeneities in the plans, and although various measures for mitigating these are already available, it is of fundamental interest to understand their cause. We have also shown that the relationship between the objective function of the linear penalty model and the measures commonly used for evaluating the quality of the dose distribution is weak. This implies that even if the model is solved to optimality there is no guarantee that the generated plan is optimal with respect to clinically relevant objectives, or even near-optimal. We have therefore constructed a new model for optimizing the dwelling time pattern. This model approximates the quality measures by the concept conditional value-at-risk, and we show that the relationship between our new model and the quality measures is strong. Furthermore, the new model generates dwelling time patterns that yield high-quality dose distributions. Combining optimization of the dwelling time pattern with optimization of the catheter positioning yields a problem for which it is rarely possible to find a proven optimal solution within a reasonable time frame. We have therefore developed a variable neighbourhood search heuristic that outperforms a state-of-the-art optimization software (CPLEX). We have also developed a tailored branch-and-bound algorithm that is better at improving the dual bound than a general branch-and-bound algorithm. This is a step towards the development of a method that can find proven optimal solutions to the combined problem within a reasonable time frame.
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Najafiazar, Bahador. "Mathematical Optimization in Reservoir Management." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for petroleumsteknologi og anvendt geofysikk, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-27058.

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Getting the most out of a hydrocarbon reservoir is not a trivial task. It takes plentyof interwoven decisions to make. There are many forms of tools that support engineersto make correct decisions. The simplest ones would only display measurementsin a suitable way, and appoint the rest of the decision making processto human knowledge and experience. Complex decision support tools may implementmodel-based estimation and optimization. This work targets methods foroptimization-based decision support.The objective of this study is to formulate, implement and test promising methodsof hydrocarbon production optimization through various test cases. To do this, avarious optimizations algorithm were applied to the simulated reservoir modelsusing the Matlab Reservoir Simulation Toolbox (MRST).
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Saunders, David. "Applications of optimization to mathematical finance." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq29265.pdf.

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Chang, Tyler Hunter. "Mathematical Software for Multiobjective Optimization Problems." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/98915.

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In this thesis, two distinct problems in data-driven computational science are considered. The main problem of interest is the multiobjective optimization problem, where the tradeoff surface (called the Pareto front) between multiple conflicting objectives must be approximated in order to identify designs that balance real-world tradeoffs. In order to solve multiobjective optimization problems that are derived from computationally expensive blackbox functions, such as engineering design optimization problems, several methodologies are combined, including surrogate modeling, trust region methods, and adaptive weighting. The result is a numerical software package that finds approximately Pareto optimal solutions that are evenly distributed across the Pareto front, using minimal cost function evaluations. The second problem of interest is the closely related problem of multivariate interpolation, where an unknown response surface representing an underlying phenomenon is approximated by finding a function that exactly matches available data. To solve the interpolation problem, a novel algorithm is proposed for computing only a sparse subset of the elements in the Delaunay triangulation, as needed to compute the Delaunay interpolant. For high-dimensional data, this reduces the time and space complexity of Delaunay interpolation from exponential time to polynomial time in practice. For each of the above problems, both serial and parallel implementations are described. Additionally, both solutions are demonstrated on real-world problems in computer system performance modeling.<br>Doctor of Philosophy<br>Science and engineering are full of multiobjective tradeoff problems. For example, a portfolio manager may seek to build a financial portfolio with low risk, high return rates, and minimal transaction fees; an aircraft engineer may seek a design that maximizes lift, minimizes drag force, and minimizes aircraft weight; a chemist may seek a catalyst with low viscosity, low production costs, and high effective yield; or a computational scientist may seek to fit a numerical model that minimizes the fit error while also minimizing a regularization term that leverages domain knowledge. Often, these criteria are conflicting, meaning that improved performance by one criterion must be at the expense of decreased performance in another criterion. The solution to a multiobjective optimization problem allows decision makers to balance the inherent tradeoff between conflicting objectives. A related problem is the multivariate interpolation problem, where the goal is to predict the outcome of an event based on a database of past observations, while exactly matching all observations in that database. Multivariate interpolation problems are equally as prevalent and impactful as multiobjective optimization problems. For example, a pharmaceutical company may seek a prediction for the costs and effects of a proposed drug; an aerospace engineer may seek a prediction for the lift and drag of a new aircraft design; or a search engine may seek a prediction for the classification of an unlabeled image. Delaunay interpolation offers a unique solution to this problem, backed by decades of rigorous theory and analytical error bounds, but does not scale to high-dimensional "big data" problems. In this thesis, novel algorithms and software are proposed for solving both of these extremely difficult problems.
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ROSSI, FILIPPO. "Mathematical models for selling process optimization." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1050078.

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The work of the Thesis has been pursued in collaboration with an important company operating in the tourist sector. The followed projects in the work can be seen as belonging to the Destination Management branch, that is the study and the implementation of actions aimed at better managing the company offer related to touristic experiences broadly. In particular, the first project has been related to Revenue Forecasting and has dealt with the definition of a methodology, based on mathematical and statistical techniques, aimed at forecasting the revenue streams linked to specific items of a company; the second project, Destination Discovery, instead aimed at the high-level analysis of tourism opportunities in different geographical areas, researching and evaluating new possibilities for the company related to tourist interest. In the work, some preliminaries about what a forecast is will be provided and the many techniques aimed at accomplishing the task, giving a general theoretical framework for the topic will be discussed. Then some details about data and the set of more practical operations needed in order to extract information from them in a numerical manner, eventually building a forecasting model on it will be discussed. Later the application of the techniques previously introduced to the different projects will be discussed; for each one of them, the methodologies followed and the analyzes carried out will be provided, as well as the obtained results. Finally an analysis of what has globally been done in the work along with different comments, the obtained results and some possible future work and improvements will conclude the work.
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Rossetti, Gaia. "Mathematical optimization techniques for cognitive radar networks." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/33419.

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This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise.
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Trescher, Saskia. "Estimating Gene Regulatory Activity using Mathematical Optimization." Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21900.

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Die Regulation der Genexpression ist einer der wichtigsten zellulären Prozesse und steht in Zusammenhang mit der Entstehung diverser Krankheiten. Regulationsmechanismen können mit einer Vielzahl von Methoden experimentell untersucht werden, zugleich erfordert die Integration der Datensätze in umfassende Modelle stringente rechnergestützte Methoden. Ein Teil dieser Methoden modelliert die genomweite Genexpression als (lineares) Gleichungssystem über die Aktivität und Beziehungen von Transkriptionsfaktoren (TF), Genen und anderen Faktoren und optimiert die Parameter, sodass die gemessenen Expressionsintensitäten möglichst genau wiedergegeben werden. Trotz ihrer gemeinsamen Wurzeln in der mathematischen Optimierung unterscheiden sich die Methoden stark in der Art der integrierten Daten, im für ihre Anwendung notwendigen Hintergrundwissen, der Granularität des Regulationsmodells, des konkreten Paradigmas zur Lösung des Optimierungsproblems, und der zur Evaluation verwendeten Datensätze. In dieser Arbeit betrachten wir fünf solcher Methoden und stellen einen qualitativen und quantitativen Vergleich auf. Unsere Ergebnisse zeigen, dass die Überschneidungen der Ergebnisse sehr gering sind, was nicht auf die Stichprobengröße oder das regulatorische Netzwerk zurückgeführt werden kann. Ein Grund für die genannten Defizite könnten die vereinfachten Modelle zellulärer Prozesse sein, da diese vorhandene Rückkopplungsschleifen ignorieren. Wir schlagen eine neue Methode (Florae) mit Schwerpunkt auf die Berücksichtigung von Rückkopplungsschleifen vor und beurteilen deren Ergebnisse. Mit Floræ können wir die Identifizierung von Knockout- und Knockdown-TF in synthetischen Datensätzen verbessern. Unsere Ergebnisse und die vorgeschlagene Methode erweitern das Wissen über genregulatorische Aktivität können die Identifizierung von Ursachen und Mechanismen regulatorischer (Dys-)Funktionen und die Entwicklung von medizinischen Biomarkern und Therapien unterstützen.<br>Gene regulation is one of the most important cellular processes and closely interlinked pathogenesis. The elucidation of regulatory mechanisms can be approached by many experimental methods, yet integration of the resulting heterogeneous, large, and noisy data sets into comprehensive models requires rigorous computational methods. A prominent class of methods models genome-wide gene expression as sets of (linear) equations over the activity and relationships of transcription factors (TFs), genes and other factors and optimizes parameters to fit the measured expression intensities. Despite their common root in mathematical optimization, they vastly differ in the types of experimental data being integrated, the background knowledge necessary for their application, the granularity of their regulatory model, the concrete paradigm used for solving the optimization problem and the data sets used for evaluation. We review five recent methods of this class and compare them qualitatively and quantitatively in a unified framework. Our results show that the result overlaps are very low, though sometimes statistically significant. This poor overall performance cannot be attributed to the sample size or to the specific regulatory network provided as background knowledge. We suggest that a reason for this deficiency might be the simplistic model of cellular processes in the presented methods, where TF self-regulation and feedback loops were not represented. We propose a new method for estimating transcriptional activity, named Florae, with a particular focus on the consideration of feedback loops and evaluate its results. Using Floræ, we are able to improve the identification of knockout and knockdown TFs in synthetic data sets. Our results and the proposed method extend the knowledge about gene regulatory activity and are a step towards the identification of causes and mechanisms of regulatory (dys)functions, supporting the development of medical biomarkers and therapies.
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Haddon, Antoine. "Mathematical Modeling and Optimization for Biogas Production." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS047.

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La digestion anaérobique est un processus biologique au cours duquel des micro-organismes décomposent de la matière organique pour produire du biogaz (dioxyde de carbone et methane) qui peut être utilisé comme source d'énergie renouvelable. Cette thèse porte sur l'élaboration de stratégies de contrôle et la conception de bioréacteurs qui maximisent la production de biogaz.La première partie se concentre sur le problème de contrôle optimal de la maximisation de la production de biogaz dans un chemostat avec un modèle à une réaction, en contrôlant le taux de dilution. Pour le problème à horizon fini, nous étudions des commandes type feedback, similaires à ceux utilisés en pratique et consistant à conduire le réacteur vers un niveau de substrat donné et à le maintenir à ce niveau. Notre approche repose sur une estimation de la fonction de valeur inconnue en considérant différentes fonctions de coût pour lesquelles la solution optimale admet un feedback optimal explicite et autonome. En particulier, cette technique fournit une estimation de la sous-optimalité des régulateurs étudiés pour une large classe de fonctions de croissance dépendant du substrat et de la biomasse. À l'aide de simulations numériques, on montre que le choix du meilleur feedback dépend de l'horizon de temps et de la condition initiale.Ensuite, nous examinons le problème sur un horizon infini, pour les coûts moyen et actualisé. On montre que lorsque le taux d'actualisation tends vers à 0, la fonction de valeur du problème actualisé converge vers la fonction de valeur pour le coût moyen. On identifie un ensemble de solutions optimales pour le problème de limite et avec coût moyen comme étant les contrôles qui conduisent le système vers un état qui maximise le débit de biogaz sur un ensemble invariant.Nous revenons ensuite au problème sur à horizon fini fixe et avec le Principe du Maximum de Pontryagin, on montre que le contrôle optimal à une structure bang arc singulier. On construit une famille de contrôles extremal qui dépendent de la valeur constante du Hamiltonien. En utilisant l'équation de Hamilton-Jacobi-Bellman, on identifie le contrôle optimal comme étant celui associé à la valeur du Hamiltonien qui satisfait une équation de point fixe. On propose ensuite un algorithme pour calculer la commande optimale en résolvant cette équation de point fixe. On illustre enfin cette méthode avec les deux principales types de fonctions de croissance de Monod et Haldane.Dans la deuxième partie, on modélise et on étudie l'impact de l'hétérogénéité du milieu réactionnel sur la production de biogaz. Pour cela, on introduit un modèle de bioréacteur pilote qui décrit les caractéristiques spatiales. Ce modèle tire parti de la géométrie du réacteur pour réduire la dimension spatiale de la section contenant un lit fixe et, dans les autres sections, on considère les équations 3D de Navier-Stokes en régime permanent pour la dynamique des fluides. Pour représenter l'activité biologique, on utilise un modèle à deux réactions et pour les substrats, des équations advection-diffusion-réaction. On considère seulement les biomasses qui sont attachées au lit fixe et on modélise leur croissance avec une fonction densité dépendante. On montre que ce modèle peut reproduire le gradient spatial de données expérimentales et permet de mieux comprendre la dynamique interne du réacteur. En particulier, les simulations numériques indiquent qu'en mélangeant moins, le réacteur est plus efficace, élimine plus de matières organiques et produit plus de biogaz<br>Anaerobic digestion is a biological process in which organic compounds are degraded by different microbial populations into biogas (carbon dioxyde and methane), which can be used as a renewable energy source. This thesis works towards developing control strategies and bioreactor designs that maximize biogas production.The first part focuses on the optimal control problem of maximizing biogas production in a chemostat in several directions. We consider the single reaction model and the dilution rate is the controlled variable.For the finite horizon problem, we study feedback controllers similar to those used in practice and consisting in driving the reactor towards a given substrate level and maintaining it there. Our approach relies on establishing bounds of the unknown value function by considering different rewards for which the optimal solution has an explicit optimal feedback that is time-independent. In particular, this technique provides explicit bounds on the sub-optimality of the studied controllers for a broad class of substrate and biomass dependent growth rate functions. With numerical simulations, we show that the choice of the best feedback depends on the time horizon and initial condition.Next, we consider the problem over an infinite horizon, for averaged and discounted rewards. We show that, when the discount rate goes to 0, the value function of the discounted problem converges and that the limit is equal to the value function for the averaged reward. We identify a set of optimal solutions for the limit and averaged problems as the controls that drive the system towards a state that maximizes the biogas flow rate on an special invariant set.We then return to the problem over a fixed finite horizon and with the Pontryagin Maximum Principle, we show that the optimal control has a bang singular arc structure. We construct a one parameter family of extremal controls that depend on the constant value of the Hamiltonian. Using the Hamilton-Jacobi-Bellman equation, we identify the optimal control as the extremal associated with the value of the Hamiltonian which satisfies a fixed point equation. We then propose a numerical algorithm to compute the optimal control by solving this fixed point equation. We illustrate this method with the two major types of growth functions of Monod and Haldane.In the second part, we investigate the impact of mixing the reacting medium on biogas production. For this we introduce a model of a pilot scale upflow fixed bed bioreactor that offers a representation of spatial features. This model takes advantage of reactor geometry to reduce the spatial dimension of the section containing the fixed bed and in other sections, we consider the 3D steady-state Navier-Stokes equations for the fluid dynamics. To represent the biological activity, we use a 2 step model and for the substrates, advection-diffusion-reaction equations. We only consider the biomasses that are attached in the fixed bed section and we model their growth with a density dependent function. We show that this model can reproduce the spatial gradient of experimental data and helps to better understand the internal dynamics of the reactor. In particular, numerical simulations indicate that with less mixing, the reactor is more efficient, removing more organic matter and producing more biogas
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Books on the topic "Mathematical optimization"

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Snyman, Jan A., and Daniel N. Wilke. Practical Mathematical Optimization. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77586-9.

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L, Rardin Ronald, ed. Discrete optimization. Boston: Academic Press, 1988.

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Dingzhu, Du, Pardalos P. M. 1954-, and Wu Weili, eds. Mathematical theory of optimization. Dordrecht: Kluwer Academic, 2001.

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Hoffmann, Karl-Heinz, Jochem Zowe, Jean-Baptiste Hiriart-Urruty, and Claude Lemarechal, eds. Trends in Mathematical Optimization. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9297-1.

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Pallaschke, Diethard, and Stefan Rolewicz. Foundations of Mathematical Optimization. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-1588-1.

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Hürlimann, Tony. Mathematical Modeling and Optimization. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-5793-4.

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Du, Ding-Zhu, Panos M. Pardalos, and Weili Wu, eds. Mathematical Theory of Optimization. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-5795-8.

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Oberwolfach), Tagung Methoden und Verfahren der Mathematischen Physik (11th 1985 Mathematisches Forschungsinstitut. Optimization in mathematical physics. Frankfurt am Main: P. Lang, 1987.

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Du, Dingzhu. Mathematical Theory of Optimization. Boston, MA: Springer US, 2001.

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Guddat, Jürgen. Multiobjective and stochastic optimization based on parametric optimization. Berlin: Akademie-Verlag, 1985.

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Book chapters on the topic "Mathematical optimization"

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Schittkowski, Klaus. "Mathematical Optimization." In Software Systems for Structural Optimization, 33–42. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8553-9_2.

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Wang, Liang, and Jianxin Zhao. "Mathematical Optimization." In Architecture of Advanced Numerical Analysis Systems, 87–119. Berkeley, CA: Apress, 2022. http://dx.doi.org/10.1007/978-1-4842-8853-5_4.

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Pappalardo, Elisa, Panos M. Pardalos, and Giovanni Stracquadanio. "Mathematical Optimization." In SpringerBriefs in Optimization, 13–25. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9053-1_3.

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Cao, Bing-Yuan. "Mathematical Preliminaries." In Applied Optimization, 1–22. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0009-4_1.

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Kogan, Konstantin, and Eugene Khmelnitsky. "Mathematical Background." In Applied Optimization, 19–35. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4675-7_2.

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Schittkowski, Klaus. "Mathematical Foundations." In Applied Optimization, 7–118. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4419-5762-7_2.

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Belenky, Alexander S. "Mathematical Programming." In Applied Optimization, 13–90. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6075-0_2.

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Lobato, Fran Sérgio, and Valder Steffen. "Mathematical." In Multi-Objective Optimization Problems, 77–108. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58565-9_5.

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Neumaier, Arnold. "Mathematical Model Building." In Applied Optimization, 37–43. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4613-0215-5_3.

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Bhatti, M. Asghar. "Mathematical Preliminaries." In Practical Optimization Methods, 75–129. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0501-2_3.

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Conference papers on the topic "Mathematical optimization"

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Chen, Guoxin, Minpeng Liao, Chengxi Li, and Kai Fan. "Step-level Value Preference Optimization for Mathematical Reasoning." In Findings of the Association for Computational Linguistics: EMNLP 2024, 7889–903. Stroudsburg, PA, USA: Association for Computational Linguistics, 2024. http://dx.doi.org/10.18653/v1/2024.findings-emnlp.463.

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Zhao, Xueliang, Xinting Huang, Wei Bi, and Lingpeng Kong. "SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving." In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 7544–65. Stroudsburg, PA, USA: Association for Computational Linguistics, 2024. http://dx.doi.org/10.18653/v1/2024.acl-long.407.

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Santhamoorthy, Pooja Zen, and Selen Cremaschi. "Mathematical Optimization of Separator Network Design for Sand Management." In Foundations of Computer-Aided Process Design, 892–98. Hamilton, Canada: PSE Press, 2024. http://dx.doi.org/10.69997/sct.154881.

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Sand produced along with well-production fluids accumulates in the surface facilities over time, taking valuable space, while the sand carried with the fluids damages downstream equipment. Thus, sand is separated from the fluid in the sand traps and separators and removed during periodic clean-ups. But at high sand productions, the probability of unscheduled facilities shutdowns increases. Such extreme production conditions can be handled by strategic planning and optimal design of the separator network to enable maximum sand separation at minimal equipment cost while ensuring the accumulation extent is within tolerable limits. This paper develops a mathematical model to optimize the separator network design to maximize sand separation while the sand accumulation extent and total equipment cost are minimal. The optimization model is formulated using multi-objective mixed-integer nonlinear programming (MINLP). The capabilities of the developed model to assist sand management in the separator network are demonstrated with a case study of optimizing the network for two wells producing sand particles of different sizes. A residence time distribution-based model is used to predict sand settling behavior. The developed Pareto Front shows the trade-off between the increase in total sand accumulation rate and total equipment cost for an increase in the fraction of sand settled.
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De Kock, D. J., M. Nagulapally, J. A. Visser, R. Nair, and J. Nigen. "Mathematical Optimization of Electronic Enclosures." In ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems collocated with the ASME 2005 Heat Transfer Summer Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/ipack2005-73185.

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The thermal design of electronic enclosures is becoming more important as the demand for smaller, lighter systems with better performance increases. The limiting factor on the lifetime of these systems is the maximum temperature of the electronic components. Nowadays in some systems, the thermal design is the limiting factor for performance increases. A simple yet effective design method that yields optimum designs is therefore required to design these systems. Traditionally, experimental methods were used in the design of electronic enclosures. More recently Computational Fluid Dynamics (CFD) has established itself as a viable alternative to reduce the number of experimentation required, resulting in a reduction in the time scales and cost of the design process. The CFD process is usually applied on a trial and error basis and relies heavily on the insight and experience of the designer to improve designs. Even an experienced designer will only be able to improve the design and does not necessarily guarantee optimum results. A more efficient design method is to combine a mathematical optimizer with CFD. In this study the mathematical optimization method, DYNAMIC-Q, is linked with the commercial CFD package, Icepak to optimize different electronic enclosures. The method is applied to the following design situations commonly found in electronics enclosures. The first case is that of the optimization outlet grille of a telecommunications rack to reduce the electromagnetic interference without exceeding a specified temperature in the rack. The second case involves the optimum placement of electronic components on a printed circuit board to minimize the maximum temperatures of the components. The third case deals with flow through an electronic enclosure cooled by fans placed on the wall of the enclosures. The geometrical arrangement of boards and components on the boards in these enclosures might result in unequal flow distribution between the boards. For this purpose air flow filters of varying free-area ratios are used to make the flow rates between the boards more uniform. The free-area ratios of three filters are determined in order to maximize the total flow rate through system with the added constraint that the flow rates through each of the three filters are within 5% of each other. The last case deals with flow through a simplified notebook where the CPU temperature is minimized by changing the position of two exhaust fans. The study shows that mathematical optimization is a powerful tool that can be combined with CFD to yield optimum designs.
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Findeisen, Bernd, Mario Schwalbe, Norman Gunther, and Lutz Stiegler. "NVH Optimization of Driveline with Mathematical Optimization Methods." In Symposium on International Automotive Technology 2013. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2013. http://dx.doi.org/10.4271/2013-26-0089.

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Poole, Daniel J., Christian B. Allen, and T. Rendall. "Metric-Based Mathematical Derivation of Aerofoil Design Variables." In 10th AIAA Multidisciplinary Design Optimization Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-0114.

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Morris, R. M., J. A. Snyman, and Josua P. Meyer. "MATHEMATICAL OPTIMIZATION OF JETS IN CROSSFLOW." In Annals of the Assembly for International Heat Transfer Conference 13. Begell House Inc., 2006. http://dx.doi.org/10.1615/ihtc13.p26.200.

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EWING, M., and V. VENKAYYA. "Structural identification using mathematical optimization techniques." In 32nd Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-1135.

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Almosa, Nadia Ali Abbas, and Ahmed Sabah Al-Jilawi. "Developing mathematical optimization models with Python." In AL-KADHUM 2ND INTERNATIONAL CONFERENCE ON MODERN APPLICATIONS OF INFORMATION AND COMMUNICATION TECHNOLOGY. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0119585.

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Lee, Eva K., Tsung-Lin Wu, Onur Seref, O. Erhun Kundakcioglu, and Panos Pardalos. "Classification and disease prediction via mathematical programming." In DATA MINING, SYSTEMS ANALYSIS AND OPTIMIZATION IN BIOMEDICINE. AIP, 2007. http://dx.doi.org/10.1063/1.2817343.

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Reports on the topic "Mathematical optimization"

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Lovianova, Iryna V., Dmytro Ye Bobyliev, and Aleksandr D. Uchitel. Cloud calculations within the optional course Optimization Problems for 10th-11th graders. [б. в.], September 2019. http://dx.doi.org/10.31812/123456789/3267.

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The article deals with the problem of introducing cloud calculations into 10th-11th graders’ training to solve optimization problems in the context of the STEM-education concept. After analyzing existing programmes of optional courses on optimization problems, the programme of the optional course Optimization Problems has been developed and substantiated implying solution of problems by the cloud environment CoCalc. It is a routine calculating operation and not a mathematical model that is accentuated in the programme. It allows considering more problems which are close to reality without adapting the material while training 10th-11th graders. Besides, the mathematical apparatus of the course which is partially known to students as the knowledge acquired from such mathematics sections as the theory of probability, mathematical statistics, mathematical analysis and linear algebra is enough to master the suggested course. The developed course deals with a whole class of problems of conventional optimization which vary greatly. They can be associated with designing devices and technological processes, distributing limited resources and planning business functioning as well as with everyday problems of people. Devices, processes and situations to which a model of optimization problem is applied are called optimization problems. Optimization methods enable optimal solutions for mathematical models. The developed course is noted for building mathematical models and defining a method to be applied to finding an efficient solution.
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Venkayya, Vipperla B., and Victoria A. Tischler. A Compound Scaling Algorithm for Mathematical Optimization. Fort Belvoir, VA: Defense Technical Information Center, February 1989. http://dx.doi.org/10.21236/ada208446.

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Eskow, Elizabeth, and Robert B. Schnabel. Mathematical Modeling of a Parallel Global Optimization Algorithm. Fort Belvoir, VA: Defense Technical Information Center, April 1988. http://dx.doi.org/10.21236/ada446514.

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Pasupuleti, Murali Krishna. Mathematical Modeling for Machine Learning: Theory, Simulation, and Scientific Computing. National Education Services, March 2025. https://doi.org/10.62311/nesx/rriv125.

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Abstract Mathematical modeling serves as a fundamental framework for advancing machine learning (ML) and artificial intelligence (AI) by integrating theoretical, computational, and simulation-based approaches. This research explores how numerical optimization, differential equations, variational inference, and scientific computing contribute to the development of scalable, interpretable, and efficient AI systems. Key topics include convex and non-convex optimization, physics-informed machine learning (PIML), partial differential equation (PDE)-constrained AI, and Bayesian modeling for uncertainty quantification. By leveraging finite element methods (FEM), computational fluid dynamics (CFD), and reinforcement learning (RL), this study demonstrates how mathematical modeling enhances AI-driven scientific discovery, engineering simulations, climate modeling, and drug discovery. The findings highlight the importance of high-performance computing (HPC), parallelized ML training, and hybrid AI approaches that integrate data-driven and model-based learning for solving complex real-world problems. Keywords Mathematical modeling, machine learning, scientific computing, numerical optimization, differential equations, PDE-constrained AI, variational inference, Bayesian modeling, convex optimization, non-convex optimization, reinforcement learning, high-performance computing, hybrid AI, physics-informed machine learning, finite element methods, computational fluid dynamics, uncertainty quantification, simulation-based AI, interpretable AI, scalable AI.
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De Silva, K. N. A mathematical model for optimization of sample geometry for radiation measurements. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1988. http://dx.doi.org/10.4095/122732.

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Xie, Haiyan, and Mangolika Bhattacharya. MATH-DT: Development of Mathematical Models for Large-Scale Nonlinear Optimization for Digital Twins Nomenclature Table. Illinois State University, 2025. https://doi.org/10.30707/1741890724.245225.

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The nomenclature table for the Mathematical Digital Twin project description systematically defines key variables, parameters, and mathematical symbols used throughout the research. The table is deposited for open access, allowing other researchers to reference and build upon the work to enhance transparency and reproducibility.
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Wegley, H. L., and J. C. Barnard. Using the NOABL flow model and mathematical optimization as a micrositing tool. Office of Scientific and Technical Information (OSTI), November 1986. http://dx.doi.org/10.2172/6979883.

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Turinsky, Paul, and Ross Hays. Development and Utilization of mathematical Optimization in Advanced Fuel Cycle Systems Analysis. Office of Scientific and Technical Information (OSTI), September 2011. http://dx.doi.org/10.2172/1024390.

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Iyer, Ananth V., Samuel Labi, Steven R. Dunlop, Dutt J. Thakkar, Sayak Mishra, Lavanya Krishna Kumar, Runjia Du, Miheeth Gala, Apoorva Banerjee, and Gokul Siddharthan. Heavy Fleet and Facilities Optimization. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317365.

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The Indiana Department of Transportation (INDOT) is responsible for timely clearance of snow on state-maintained highways in Indiana as part of its wintertime operations. For this and other maintenance purposes, the state’s subdistricts maintain 101 administrative units spread throughout the state. These units are staffed by personnel, including snow truck drivers and house snow removal trucks and other equipment. INDOT indicated a need to carry out value engineering analysis of the replacement timing of the truck fleet. To address these questions, this study carried out analysis to ascertain the appropriate truck replacement age, that is different across each of the state's three weather-based regions to minimize the truck life cycle cost. INDOT also indicated a need for research guidance in possible revisions to the administrative unit locations and optimal routes to be taken by trucks in each unit in order to reduce deadhead miles. For purposes of optimizing the truck snow routes, the study developed two alternative algorithmic approaches. The first uses mathematical programming to select work packets for trucks while ensuring that snow is cleared at all snow routes and allowing the users to identify optimal route and unit location. The second approach uses network routing concepts, such as the rural postman problem, and allows the user to change the analysis inputs, such as the number of available drivers and so on. The first approach developed using opensolver (an open source tool with excel) and the second approach coded as an electronic tool, are submitted as part of this report. Both approaches can be used by INDOT’s administrative unit managers for decision support regarding the deployment of resources for snow clearing operations and to minimize the associated costs.
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Hector Colonmer, Prabhu Ganesan, Nalini Subramanian, Dr. Bala Haran, Dr. Ralph E. White, and Dr. Branko N. Popov. OPTIMIZATION OF THE CATHODE LONG-TERM STABILITY IN MOLTEN CARBONATE FUEL CELLS: EXPERIMENTAL STUDY AND MATHEMATICAL MODELING. Office of Scientific and Technical Information (OSTI), September 2002. http://dx.doi.org/10.2172/808855.

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