Relevant bibliographies by topics / Convex and nonconvex optimisation

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

Academic literature on the topic 'Convex and nonconvex optimisation'

Author: Grafiati
Published: 11 December 2022
Last updated: 31 July 2025

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Journal articles on the topic "Convex and nonconvex optimisation"

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Martínez-legaz, J. E., and A. Seeger. "A formula on the approximate subdifferential of the difference of convex functions." Bulletin of the Australian Mathematical Society 45, no. 1 (1992): 37–41. http://dx.doi.org/10.1017/s0004972700036984.

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We give a formula on the ε−subdifferential of the difference of two convex functions. As a by-product of this formula, one recovers a recent result of Hiriart-Urruty, namely, a necessary and sufficient condition for global optimality in nonconvex optimisation.
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Gustafson, Sven-Åke. "Investigating semi-infinite programs using penalty functions and Lagrangian methods." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 28, no. 2 (1986): 158–69. http://dx.doi.org/10.1017/s0334270000005270.

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AbstractIn this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on the fact that a convex set may be represented as the intersection of closed halfspaces, while the other class is defined using the representation of the elements of a convex set as convex combinations of points and directions. Extension to nonconvex problems is given. A common technique of solving a semi-infinite program computationally is to derive necessary conditions for
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Thi, Hoai An Le, Hoai Minh Le, and Tao Pham Dinh. "Fuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithms." Advances in Data Analysis and Classification 1, no. 2 (2007): 85–104. http://dx.doi.org/10.1007/s11634-007-0011-2.

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Lanza, A., S. Morigi, I. Selesnick, and F. Sgallari. "Nonconvex nonsmooth optimization via convex–nonconvex majorization–minimization." Numerische Mathematik 136, no. 2 (2016): 343–81. http://dx.doi.org/10.1007/s00211-016-0842-x.

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Penot, J. P. "Conditioning convex and nonconvex problems." Journal of Optimization Theory and Applications 90, no. 3 (1996): 535–54. http://dx.doi.org/10.1007/bf02189795.

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Smith, E. "Global Optimisation of Nonconvex MINLPs." Computers & Chemical Engineering 21, no. 1-2 (1997): S791—S796. http://dx.doi.org/10.1016/s0098-1354(97)00146-4.

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Smith, Edward M. B., and Constantinos C. Pantelides. "Global optimisation of nonconvex MINLPs." Computers & Chemical Engineering 21 (May 1997): S791—S796. http://dx.doi.org/10.1016/s0098-1354(97)87599-0.

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Vilchez Membrilla, José Antonio, Víctor Salas Moreno, Soledad Moreno-Pulido, Alberto Sánchez-Alzola, Clemente Cobos Sánchez, and Francisco Javier García-Pacheco. "Minimization over Nonconvex Sets." Symmetry 16, no. 7 (2024): 809. http://dx.doi.org/10.3390/sym16070809.

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Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and algorithms to compute the distance of a closed convex set to the origin, which mostly exist in the Hilbert space setting. In this manuscript, we consider nonconvex minimum norm problems that arise from Bioengineering and reformulate them in such a way that the solution to their reformulation is already known. In particular, we tackle the problem o
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Eichfelder, Gabriele, and Patrick Groetzner. "A note on completely positive relaxations of quadratic problems in a multiobjective framework." Journal of Global Optimization 82, no. 3 (2021): 615–26. http://dx.doi.org/10.1007/s10898-021-01091-2.

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AbstractIn a single-objective setting, nonconvex quadratic problems can equivalently be reformulated as convex problems over the cone of completely positive matrices. In small dimensions this cone equals the cone of matrices which are entrywise nonnegative and positive semidefinite, so the convex reformulation can be solved via SDP solvers. Considering multiobjective nonconvex quadratic problems, naturally the question arises, whether the advantage of convex reformulations extends to the multicriteria framework. In this note, we show that this approach only finds the supported nondominated poi
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Keller, André A. "Convex underestimating relaxation techniques for nonconvex polynomial programming problems: computational overview." Journal of the Mechanical Behavior of Materials 24, no. 3-4 (2015): 129–43. http://dx.doi.org/10.1515/jmbm-2015-0015.

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AbstractThis paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are repla
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Dissertations / Theses on the topic "Convex and nonconvex optimisation"

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Repetti, Audrey. "Algorithmes d'optimisation en grande dimension : applications à la résolution de problèmes inverses." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1032/document.

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Une approche efficace pour la résolution de problèmes inverses consiste à définir le signal (ou l'image) recherché(e) par minimisation d'un critère pénalisé. Ce dernier s'écrit souvent sous la forme d'une somme de fonctions composées avec des opérateurs linéaires. En pratique, ces fonctions peuvent n'être ni convexes ni différentiables. De plus, les problèmes auxquels on doit faire face sont souvent de grande dimension. L'objectif de cette thèse est de concevoir de nouvelles méthodes pour résoudre de tels problèmes de minimisation, tout en accordant une attention particulière aux coûts de calc
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Sutton, Matthew William. "Variable selection and dimension reduction for structured large datasets." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/129460/1/Matthew_Sutton_Thesis.pdf.

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Recent advances in biomedical technology have allowed us to collect massive quantities of data in the hopes of gaining a better understanding of biological phenomena. This research develops new methods to tackle the challenging problem of determining which parts of these data sets provide useful information. The new methods have been used as a tool to help determine the efficacy of a new HIV vaccine.
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Garrigos, Guillaume. "Descent dynamical systems and algorithms for tame optimization, and multi-objective problems." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS191/document.

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Dans une première partie, nous nous intéressons aux systèmes dynamiques gradients gouvernés par des fonctions non lisses, mais aussi non convexes, satisfaisant l'inégalité de Kurdyka-Lojasiewicz. Après avoir obtenu quelques résultats préliminaires pour la dynamique de la plus grande pente continue, nous étudions un algorithme de descente général. Nous prouvons, sous une hypothèse de compacité, que tout suite générée par ce schéma général converge vers un point critique de la fonction. Nous obtenons aussi de nouveaux résultats sur la vitesse de convergence, tant pour les valeurs que pour les it
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Samir, Sara. "Approches coopératives pour certaines classes de problèmes d'optimisation non convexe : Algorithmes parallèles / distribués et applications." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0039.

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Dans cette thèse, nous nous intéressons au développement des approches coopératives pour la résolution de certaines classes de problèmes d'optimisation non convexe qui jouent un rôle très important de par leurs applications dans de nombreux domaines. Il s'agit de combiner plusieurs algorithmes connus sous les noms des algorithmes composants (participants). La combinaison est basée principalement sur la programmation DC (Difference of Convex Functions) et DCA (DC Algorithm) avec des métaheuristiques. Pour la conception des logiciels nous utilisons les paradigmes de la programmation parallèle et
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Ho, Vinh Thanh. "Techniques avancées d'apprentissage automatique basées sur la programmation DC et DCA." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0289/document.

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Dans cette thèse, nous développons certaines techniques avancées d'apprentissage automatique dans le cadre de l'apprentissage en ligne et de l'apprentissage par renforcement (« reinforcement learning » en anglais -- RL). L'épine dorsale de nos approches est la programmation DC (Difference of Convex functions) et DCA (DC Algorithm), et leur version en ligne, qui sont reconnues comme de outils puissants d'optimisation non convexe, non différentiable. Cette thèse se compose de deux parties : la première partie étudie certaines techniques d'apprentissage automatique en mode en ligne et la deuxième
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Ho, Vinh Thanh. "Techniques avancées d'apprentissage automatique basées sur la programmation DC et DCA." Electronic Thesis or Diss., Université de Lorraine, 2017. http://www.theses.fr/2017LORR0289.

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Dans cette thèse, nous développons certaines techniques avancées d'apprentissage automatique dans le cadre de l'apprentissage en ligne et de l'apprentissage par renforcement (« reinforcement learning » en anglais -- RL). L'épine dorsale de nos approches est la programmation DC (Difference of Convex functions) et DCA (DC Algorithm), et leur version en ligne, qui sont reconnues comme de outils puissants d'optimisation non convexe, non différentiable. Cette thèse se compose de deux parties : la première partie étudie certaines techniques d'apprentissage automatique en mode en ligne et la deuxième
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Giagkiozis, Ioannis. "Nonconvex many-objective optimisation." Thesis, University of Sheffield, 2012. http://etheses.whiterose.ac.uk/3683/.

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As many-objective optimisation problems become more prevalent, evolutionary algorithms that are based on Pareto dominance relations are slowly becoming less popular due to severe limitations that such an approach has for this class of problems. At the same time decomposition-based methods, which have been employed traditionally in mathematical programming, are consistently increasing in popularity. These developments have been led by recent research studies that show that decomposition-based algorithms have very good convergence properties compared to Pareto-based algorithms. Decomposition-bas
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Chen, Jieqiu. "Convex relaxations in nonconvex and applied optimization." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/654.

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Traditionally, linear programming (LP) has been used to construct convex relaxations in the context of branch and bound for determining global optimal solutions to nonconvex optimization problems. As second-order cone programming (SOCP) and semidefinite programming (SDP) become better understood by optimization researchers, they become alternative choices for obtaining convex relaxations and producing bounds on the optimal values. In this thesis, we study the use of these convex optimization tools in constructing strong relaxations for several nonconvex problems, including 0-1 integer programm
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Belghiti, Moulay Tayeb. "Modélisation et techniques d'optimisation en bio-informatique et fouille de données." Thesis, Rouen, INSA, 2008. http://www.theses.fr/2008ISAM0002.

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Cette thèse est particulièrement destinée à traiter deux types de problèmes : clustering et l'alignement multiple de séquence. Notre objectif est de résoudre de manière satisfaisante ces problèmes globaux et de tester l'approche de la Programmation DC et DCA sur des jeux de données réelles. La thèse comporte trois parties : la première partie est consacrée aux nouvelles approches de l'optimisation non convexe. Nous y présentons une étude en profondeur de l'algorithme qui est utilisé dans cette thèse, à savoir la programmation DC et l'algorithme DC (DCA). Dans la deuxième partie, nous allons mo
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Louchart, Arthur. "Nonlinear impairments aware resource allocation for cognitive satellite systems." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAT031.

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Cette thèse traite le problème de l’allocation de ressources pour les communications cognitives par satellite. Dans un contexte de demandes grandissantes en terme de débit, les systèmes de communication par satellite sont amenés à utiliser des fréquences déjà employées par des systèmes terrestres. Le paradigme de la radio cognitive de type sous couche permet à un réseau secondaire d'utiliser la même bande de fréquence qu'un réseau primaire. Cependant, l'interférence créée par le réseau secondaire ne doit pas excéder une certaine limite, fixée par le réseau primaire. Nous considérons un système
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Books on the topic "Convex and nonconvex optimisation"

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Michalka, Alexander. Cutting Planes for Convex Objective Nonconvex Optimization. [publisher not identified], 2013.

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Lieven, Vandenberghe, ed. Convex optimization. Cambridge University Press, 2006.

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Gao, David Yang. Duality principles in nonconvex systems: Theory, methods, and applications. Kluwer Academic Publishers, 2000.

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Gao, David Yang. Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Springer US, 2000.

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Joydeep, Dutta, ed. Optimality conditions in convex optimization: A finite-dimensional view. CRC Press, 2012.

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1941-, Cellina Arrigo, and Centro internazionale matematico estivo, eds. Methods of nonconvex analysis: Lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held at Varenna, Italy, June 15-23, 1989. Springer-Verlag, 1990.

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Bhooshan, Upadhyay Balendu, ed. Pseudolinear functions and optimization. CRC Press, Taylor & Francis Group, 2015.

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Duality in nonconvex approximation and optimization. Springer, 2005.

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Singer, Ivan. Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics). Springer, 2006.

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Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions. Birkhäuser, 2011.

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Book chapters on the topic "Convex and nonconvex optimisation"

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Tuy, Hoang. "Convex Sets." In Nonconvex Optimization and Its Applications. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2809-5_1.

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Tuy, Hoang. "Convex Functions." In Nonconvex Optimization and Its Applications. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2809-5_2.

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Rapcsák, Tamás. "Geodesic Convex Functions." In Nonconvex Optimization and Its Applications. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6357-0_6.

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Bard, Jonathan F. "Convex Bilevel Programming." In Nonconvex Optimization and Its Applications. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2836-1_7.

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Maréchal, Pierre. "Generating Convex Functions." In Nonconvex Optimization and Its Applications. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0279-7_21.

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Schofield, Norman. "Topology and Convex Optimisation." In Springer Texts in Business and Economics. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-39818-6_3.

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Schofield, Norman. "Topology and Convex Optimisation." In Mathematical Methods in Economics and Social Choice. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-55867-2_3.

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Tawarmalani, Mohit, and Nikolaos V. Sahinidis. "Convex Extensions and Relaxation Strategies." In Nonconvex Optimization and Its Applications. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3532-1_2.

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Zhang, Li-Wei, and Zun-Quan Xia. "Approximations to Convex-Valued Multifunctions." In Nonconvex Optimization and Its Applications. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3137-8_13.

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Castellani, Marco, and Massimo Pappalardo. "Characterizations of ρ-Convex Functions." In Nonconvex Optimization and Its Applications. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4613-3341-8_9.

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Conference papers on the topic "Convex and nonconvex optimisation"

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von Wrangel, David, and Russ Tedrake. "Using Graphs of Convex Sets to Guide Nonconvex Trajectory Optimization." In 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2024. https://doi.org/10.1109/iros58592.2024.10802426.

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Cho, Namhoon, and Hyo-Sang Shin. "A Passivity-Based Method for Accelerated Convex Optimisation." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10886267.

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Marousi, Asimina, and Vassilis M. Charitopoulos. "Global Robust Optimisation for Non-Convex Quadratic Programs: Application to Pooling Problems." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.168949.

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Robust optimisation is a powerful approach for addressing uncertainty ensuring constraint satisfaction for all uncertain parameter realisations. While convex robust optimisation problems are effectively tackled using robust reformulations and cutting plane methods, extending these techniques to non-convex problems remains largely unexplored. In this work we propose a method that is based on a parallel robustness and optimality search. We introduce a novel spatial Branch-and-Bound algorithm integrated with robust cutting-planes for solving non-convex robust optimisation problems. The algorithm
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Aras, Chinmay M., Ashfaq Iftakher, and M. M. Faruque Hasan. "Guaranteed Error-bounded Surrogate Framework for Solving Process Simulation Problems." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.182073.

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Process simulation problems often involve systems of nonlinear and nonconvex equations and may run into convergence issues due to the existence of recycle loops within such models. To that end, surrogate models have gained significant attention as an alternative to high-fidelity models as they significantly reduce the computational burden. However, these models do not always provide a guarantee on the prediction accuracy over the domain of interest. To address this issue, we strike a balance between computational complexity by developing a data-driven branch and prune-based framework that prog
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Lourenço, Pedro, Hugo Costa, João Branco, et al. "Verification & validation of optimisation-based control systems: methods and outcomes of VV4RTOS." In ESA 12th International Conference on Guidance Navigation and Control and 9th International Conference on Astrodynamics Tools and Techniques. ESA, 2023. http://dx.doi.org/10.5270/esa-gnc-icatt-2023-155.

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VV4RTOS is an activity supported by the European Space Agency aimed at the development and validation of a framework for the verification and validation of spacecraft guidance, navigation, and control (GNC) systems based on embedded optimisation, tailored to handle different layers of abstraction, from guidance and control (G&C) requirements down to hardware level. This is grounded on the parallel design and development of real-time optimisation-based G&C software, allowing to concurrently identify, develop, consolidate, and validate a set of engineering practices and analysis & ve
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Zhang, Roxin. "Conditioning Convex and Nonconvex Functions in Optimization." In 2012 Fifth International Joint Conference on Computational Sciences and Optimization (CSO). IEEE, 2012. http://dx.doi.org/10.1109/cso.2012.63.

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Huang, Shaoming, Yong Zhou, and Yuanming Shi. "Noisy Demixing: Convex Relaxation Meets Nonconvex Optimization." In 2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall). IEEE, 2020. http://dx.doi.org/10.1109/vtc2020-fall49728.2020.9348678.

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Scott, Joseph K., and Paul I. Barton. "Convex relaxations for nonconvex optimal control problems." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6160284.

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Li, Qiuwei, and Gongguo Tang. "Convex and nonconvex geometries of symmetric tensor factorization." In 2017 51st Asilomar Conference on Signals, Systems, and Computers. IEEE, 2017. http://dx.doi.org/10.1109/acssc.2017.8335189.

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Yang, Yang, Marius Pesavento, Zhi-Quan Luo, and Bjorn Ottersten. "Block Successive Convex Approximation Algorithms for Nonsmooth Nonconvex Optimization." In 2019 53rd Asilomar Conference on Signals, Systems, and Computers. IEEE, 2019. http://dx.doi.org/10.1109/ieeeconf44664.2019.9049006.

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Reports on the topic "Convex and nonconvex optimisation"

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Tran, Tuyen. Convex and Nonconvex Optimization Techniques for Multifacility Location and Clustering. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.7356.

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Lawrence, Nathan. Convex and Nonconvex Optimization Techniques for the Constrained Fermat-Torricelli Problem. Portland State University Library, 2016. http://dx.doi.org/10.15760/honors.319.

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