Relevant bibliographies by topics / Karush-Kuhn-Tucker conditions

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  2. Dissertations / Theses
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Academic literature on the topic 'Karush-Kuhn-Tucker conditions'

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Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Karush-Kuhn-Tucker conditions"

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Pan, Shaohua, Shujun Bi, and Jein-Shan Chen. "Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming." Abstract and Applied Analysis 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/602735.

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This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.
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Jahn, Johannes. "Karush–Kuhn–Tucker Conditions in Set Optimization." Journal of Optimization Theory and Applications 172, no. 3 (January 30, 2017): 707–25. http://dx.doi.org/10.1007/s10957-017-1066-7.

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Chen, Han, and Pasquale Malacaria. "Studying Maximum Information Leakage Using Karush-Kuhn-Tucker Conditions." Electronic Proceedings in Theoretical Computer Science 7 (October 23, 2009): 1–15. http://dx.doi.org/10.4204/eptcs.7.1.

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Khanh, Phan Quoc, and Nguyen Minh Tung. "Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization." SIAM Journal on Optimization 28, no. 1 (January 2018): 820–48. http://dx.doi.org/10.1137/16m1079920.

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Kim, Do Sang, and Nguyen Van Tuyen. "A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems." RAIRO - Operations Research 52, no. 2 (April 2018): 567–75. http://dx.doi.org/10.1051/ro/2017026.

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Abdulaleem, Najeeb. "E-invexity and generalized E-invexity in E-differentiable multiobjective programming." ITM Web of Conferences 24 (2019): 01002. http://dx.doi.org/10.1051/itmconf/20192401002.

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In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.
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Luu, Do Van, and Tran Van Su. "Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints." RAIRO - Operations Research 52, no. 2 (April 2018): 543–59. http://dx.doi.org/10.1051/ro/2017042.

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We establish Fritz John necessary conditions for local weak efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives. Under suitable constraint qualifications, Karush–Kuhn–Tucker necessary conditions for those solutions are investigated.
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Antczak, Tadeusz. "Multiobjective programming under nondifferentiable G-V-invexity." Filomat 30, no. 11 (2016): 2909–23. http://dx.doi.org/10.2298/fil1611909a.

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In the paper, new Fritz John type necessary optimality conditions and new Karush-Kuhn-Tucker type necessary opimality conditions are established for the considered nondifferentiable multiobjective programming problem involving locally Lipschitz functions. Proofs of them avoid the alternative theorem usually applied in such a case. The sufficiency of the introduced Karush-Kuhn-Tucker type necessary optimality conditions are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem are G-V-invex with respect to the same function ?. Further, the so-called nondifferentiable vector G-Mond-Weir dual problem is defined for the considered nonsmooth multiobjective programming problem. Under nondifferentiable G-V-invexity hypotheses, several duality results are established between the primal vector optimization problem and its G-dual problem in the sense of Mond-Weir.
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Haeser, Gabriel, and Alberto Ramos. "Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization." Journal of Optimization Theory and Applications 187, no. 2 (September 29, 2020): 469–87. http://dx.doi.org/10.1007/s10957-020-01749-z.

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Chalco-Cano, Y., W. A. Lodwick, R. Osuna-Gómez, and A. Rufián-Lizana. "The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems." Fuzzy Optimization and Decision Making 15, no. 1 (April 23, 2015): 57–73. http://dx.doi.org/10.1007/s10700-015-9213-9.

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Dissertations / Theses on the topic "Karush-Kuhn-Tucker conditions"

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Oliveira, Fabiana Rodrigues de. "Estudo de alguns métodos clássicos de otimização restrita não linear." Universidade Federal de Uberlândia, 2012. https://repositorio.ufu.br/handle/123456789/16795.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work some classical methods for constrained nonlinear optimization are studied. The mathematical formulations for the optimization problem with equality and inequality constrained, convergence properties and algorithms are presented. Furthermore, optimality conditions of rst order (Karush-Kuhn-Tucker conditions) and of second order. These conditions are essential for the demonstration of many results. Among the methods studied, some techniques transform the original problem into an unconstrained problem (Penalty Methods, Augmented Lagrange Multipliers Method). In others methods, the original problem is modeled as one or as a sequence of quadratic subproblems subject to linear constraints (Quadratic Programming Method, Sequential Quadratic Programming Method). In order to illustrate and compare the performance of the methods studied, two nonlinear optimization problems are considered: a bi-dimensional problem and a problem of mass minimization of a coil spring. The obtained results are analyzed and confronted with each other.
Neste trabalho são estudados alguns métodos clássicos de otimização restrita não linear. São abordadas a formulação matemática para o problema de otimização com restrições de igualdade e desigualdade, propriedades de convergência e algoritmos. Além disso, são relatadas as condições de otimalidade de primeira ordem (condições de Karush-Kuhn-Tucker) e de segunda ordem. Estas condições são essenciais para a demonstração de muitos resultados. Dentre os métodos estudados, algumas técnicas transformam o problema original em um problema irrestrito (Métodos de Penalidade, Método dos Multiplicadores de Lagrange Aumentado). Em outros métodos, o problema original é modelado como um ou uma seqüência de subproblemas quadráticos sujeito _a restrições lineares (Método de Programação Quadrática, Método de Programação Quadrática Seqüencial). A fim de ilustrar e comparar o desempenho dos métodos estudados são considerados dois problemas de otimização não linear: um problema bidimensional e o problema de minimização da massa de uma mola helicoidal. Os resultados obtidos são examinados e confrontados entre si.
Mestre em Matemática
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Hošek, Jaromír. "Optimalizační modely pro energetické využití odpadu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232178.

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The main aim of this thesis is to create a sequence of mathematical optimization models with different levels of complexity for the efficient management and waste energy utilization. Stochastic programming approach was utilized to deal with random demand and uncertain heating values. Hence, more applicable model of the waste-to-energy plant has been developed. As the next step, the model is enhanced by heating plant extension. Computations are realized for real-world data and optimal solution is found by using GAMS implementation.
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Yucel, Gizem. "A Reactionary Obstacle Avoidance Algorithm For Autonomous Vehicles." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614480/index.pdf.

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This thesis focuses on the development of guidance algorithms in order to avoid a prescribed obstacle primarily using the Collision Cone Method (CCM). The Collision Cone Method is a geometric approach to obstacle avoidance, which forms an avoidance zone around the obstacles for the vehicle to pass the obstacle around this zone. The method is reactive as it helps to avoid the pop-up obstacles as well as the known obstacles and local as it passes the obstacles and continue to the prescribed trajectory. The algorithm is first developed for a 2D (planar) avoidance in 3D environment and then extended for 3D scenarios. The algorithm is formed for the optimized CCM as well. The avoidance zone radius and velocity are optimized using constraint optimization, Lagrange multipliers with Karush-Kuhn-Tucker conditions and direct experimentation.
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Villanueva, Fabiola Roxana. "Contributions in interval optimization and interval optimal control /." São José do Rio Preto, 2020. http://hdl.handle.net/11449/192795.

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Orientador: Valeriano Antunes de Oliveira
Resumo: Neste trabalho, primeiramente, serão apresentados problemas de otimização nos quais a função objetivo é de múltiplas variáveis e de valor intervalar e as restrições de desigualdade são dadas por funcionais clássicos, isto é, de valor real. Serão dadas as condições de otimalidade usando a E−diferenciabilidade e, depois, a gH−diferenciabilidade total das funções com valor intervalar de várias variáveis. As condições necessárias de otimalidade usando a gH−diferenciabilidade total são do tipo KKT e as suficientes são do tipo de convexidade generalizada. Em seguida, serão estabelecidos problemas de controle ótimo nos quais a funçãao objetivo também é com valor intervalar de múltiplas variáveis e as restrições estão na forma de desigualdades e igualdades clássicas. Serão fornecidas as condições de otimalidade usando o conceito de Lipschitz para funções intervalares de várias variáveis e, logo, a gH−diferenciabilidade total das funções com valor intervalar de várias variáveis. As condições necessárias de otimalidade, usando a gH−diferenciabilidade total, estão na forma do célebre Princípio do Máximo de Pontryagin, mas desta vez na versão intervalar.
Abstract: In this work, firstly, it will be presented optimization problems in which the objective function is interval−valued of multiple variables and the inequality constraints are given by classical functionals, that is, real−valued ones. It will be given the optimality conditions using the E−differentiability and then the total gH−differentiability of interval−valued functions of several variables. The necessary optimality conditions using the total gH−differentiability are of KKT−type and the sufficient ones are of generalized convexity type. Next, it will be established optimal control problems in which the objective function is also interval−valued of multiple variables and the constraints are in the form of classical inequalities and equalities. It will be furnished the optimality conditions using the Lipschitz concept for interval−valued functions of several variables and then the total gH−differentiability of interval−valued functions of several variables. The necessary optimality conditions using the total gH−differentiability is in the form of the celebrated local Pontryagin Maximum Principle, but this time in the intervalar version.
Doutor
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Mehlitz, Patrick. "Optimierung in normierten Räumen." Thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2013. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-119320.

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Die Arbeit abstrahiert bekannte Konzepte der endlichdimensionalen Optimierung im Hinblick auf deren Anwendung in Banachräumen. Hierfür werden zunächst grundlegende Elemente der Funktionalanalysis wie schwache Konvergenz, Dualräume und Reflexivität vorgestellt. Anschließend erfolgt eine kurze Einführung in die Thematik der Fréchet-Differenzierbarkeit und eine Abstraktion des Begriffs der partiellen Ordnungsrelation in normierten Räumen. Nach der Formulierung eines allgemeinen Existenzsatzes für globale Optimallösungen von abstrakten Optimierungsaufgaben werden notwendige Optimalitätsbedingungen vom Karush-Kuhn-Tucker-Typ hergeleitet. Abschließend wird eine hinreichende Optimalitätsbedingung vom Karush-Kuhn-Tucker-Typ unter verallgemeinerten Konvexitätsvoraussetzungen verifiziert.
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Javad, Mirzaei. "Sum-rate maximization for active channels." Thesis, 2013. http://hdl.handle.net/10155/308.

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In conventional wireless channel models, there is no control on the gains of different subchannels. In such channels, the transmitted signal undergoes attenuation and phase shift and is subject to multi-path propagation effects. We herein refer to such channels as passive channels. In this dissertation, we study the problem of joint power allocation and channel design for a parallel channel which conveys information from a source to a destination through multiple orthogonal subchannels. In such a link, the power over each subchannel can be adjusted not only at the source but also at each subchannel. We refer to this link as an active parallel channel. For such a channel, we study the problem of sum-rate maximization under the assumption that the source power as well as the energy of the active channel are constrained. This problem is investigated for equal and unequal noise power at different subchannels. For equal noise power over different subchannels, although the sum-rate maximization problem is not convex, we propose a closed-form solution to this maximization problem. An interesting aspect of this solution is that it requires only a subset of the subchannels to be active and the remaining subchannels should be switched off. This is in contrast with passive parallel channels with equal subchannel signal-tonoise- ratios (SNRs), where water-filling solution to the sum-rate maximization under a total source power constraint leads to an equal power allocation among all subchannels. Furthermore, we prove that the number of active channels depends on the product of the source and channel powers. We also prove that if the total power available to the source and to the channel is limited, then in order to maximize the sum-rate via optimal power allocation to the source and to the active channel, half viii ix of the total available power should be allocated to the source and the remaining half should be allocated to the active channel. We extend our analysis to the case where the noise powers are unequal over different subchannels. we show that the sum-rate maximization problem is not convex. Nevertheless, with the aid of Karush-Kuhn-Tucker (KKT) conditions, we propose a computationally efficient algorithm for optimal source and channel power allocation. To this end, first, we obtain the feasible number of active subchannels. Then, we show that the optimal solution can be obtained by comparing a finite number of points in the feasible set and by choosing the best point which yields the best sum-rate performance. The worst-case computational complexity of this solution is linear in terms of number of subchannels.
UOIT
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Book chapters on the topic "Karush-Kuhn-Tucker conditions"

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Peressini, Anthony L., J. J. Uhl, and Francis E. Sullivan. "Convex Programming and the Karush-Kuhn-Tucker Conditions." In The Mathematics of Nonlinear Programming, 156–214. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1025-2_5.

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French, Mark. "General Conditions for Solving Optimization Problems: Karush-Kuhn-Tucker Conditions." In Fundamentals of Optimization, 143–57. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76192-3_6.

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Zhang, Ying, Xizhao Wang, and Junhai Zhai. "A Fast Support Vector Machine Classification Algorithm Based on Karush-Kuhn-Tucker Conditions." In Lecture Notes in Computer Science, 382–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10646-0_46.

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"Karush-Kuhn-Tucker (KKT) Conditions." In Encyclopedia of Operations Research and Management Science, 833–34. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_200359.

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"4 Karush–Kuhn–Tucker conditions and duality." In Nonlinear Programming, 69–108. De Gruyter, 2014. http://dx.doi.org/10.1515/9783110315288.69.

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"The Fritz John and Karush-Kuhn-tucker Optimality Conditions." In Nonlinear Programming, 163–236. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2005. http://dx.doi.org/10.1002/0471787779.ch4.

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Conference papers on the topic "Karush-Kuhn-Tucker conditions"

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Ali, Yasir, Zhen Shen, Fenghua Zhu, Gang Xiong, Shichao Chen, Yuanqing Xia, and Fei-Yue Wang. "Solutions Verification for Cloud-Based Networked Control System using Karush-Kuhn-Tucker Conditions." In 2018 Chinese Automation Congress (CAC). IEEE, 2018. http://dx.doi.org/10.1109/cac.2018.8623109.

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Chalco-Cano, Y., W. A. Lodwick, and H. Roman-Flores. "The Karush-Kuhn-Tucker optimality conditions for a class of fuzzy optimization problems using strongly generalized derivative." In 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). IEEE, 2013. http://dx.doi.org/10.1109/ifsa-nafips.2013.6608400.

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Hsu, Yeh-Liang. "Notes on Interpreting Monotonicity Analysis Using Karush-Kuhn-Tucker Conditions and MONO: A Logic Program for Monotonicity Analysis." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0397.

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Abstract The Monotonicity Principles are only necessary conditions. All principles are under the condition “if the problem is well constrained”. But one of the important purposes of Monotonicity Analysis is to identify optimization models that are not well constrained. Before applying Monotonicity Principles to a problem, whether the problem is well constrained is not known. This paper attempts to clarify some potential problems of Monotonicity Analysis when applying to not-well-constrained problems. These problems can be easily explained using the Karush-Kuhn-Tucker optimality conditions. Ways to prevent the users from reaching erroneous results in these situations are proposed. These results are implemented in the computer program MONO. MONO is a logic program which automatically generates rigorous Monotonicity Analysis steps and global facts about the optimization model. Hardware and software requirements of this program are minimal. A hydraulic cylinder design example is used to demonstrate the program.
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Dong, Jiawei, and Won-jong Kim. "Bandwidth Allocation of Networked Control Systems With Exponential Approximation." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3778.

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This paper investigates bandwidth allocation of networked control systems (NCSs) with nonlinear-programming techniques. The bandwidth utilization (BU) is defined in terms of sampling frequency. An exponential approximation is formulated to describe system performance versus the sampling frequencies. The optimal sampling frequencies are obtained by solving the approximation with Karush-Kuhn-Tucker (KKT) conditions. Simulation and experimental results verify the effectiveness of the proposed approximation. The exponential approximation can minimize the BU so that the plants can be scheduled along with the system PIFs being optimized.
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Rao, J. R. Jagannatha, and Panos Y. Papalambros. "Remarks on Conditions for the Validity of Parametric Decomposition in Optimal Design." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0049.

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Abstract Decomposition strategies are used in a variety of practical design optimization applications. Such decompositions are valid, if the solution of the decomposed problem is in fact also the solution to the original one. Conditions for such validity are not always obvious. In the present article, we develop conditions for two-level parametric decomposition under which: (1) isolated minima at the two levels imply an isolated minimum for the original problem; (2) necessary conditions at the two-levels are equivalent to the necessary conditions for the original problem; and, (3) a descent algorithm for computing Karush-Kuhn-Tucker points in decomposition formulations is globally convergent. Since no special problem structure is assumed, the results are general and could be used to evaluate the suitability of a variety of approaches and algorithms for decomposition strategies.
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Williams, Brian C., and Jonathan Cagan. "Activity Analysis: Simplifying Optimal Design Problems Through Qualitative Partitioning." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0179.

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Abstract Activity analysis is introduced as a means to strategically cut away subspaces of a design problem that can quickly be ruled out as suboptimal. This results in focused regions of the space in which additional symbolic or numerical analysis can take place. Activity analysis is derived from a qualitative abstraction of the Karush-Kuhn-Tucker conditions of optimality, used to partition an optimization problem into regions which are nonstationary and qualitatively stationary (qstationary). Activity analysis draws from the fields of gradient-based optimization, conflict-based approaches of combinatorial satisficing search, and monotonicity analysis.
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Kanakasabai, Pugazhendhi, and Anoop K. Dhingra. "An Approach for Uni-Level Reliability Based Design Optimization Using Cross-Entropy Method." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70691.

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In this paper a novel approach is proposed to solve the reliability based design optimization (RBDO) problem, which is translated into a single-level problem using Karush-Kuhn-Tucker (KKT) conditions. The transformation of a bi-level RBDO problem into a single-level problem using KKT conditions introduces several equality constraints in the single-level problem definition. Presence of multiple equality constraints poses numerical difficulty to the gradient based optimizers, hence a robust algorithm to solve the single-level RBDO problem is proposed in this paper using an alternative approach. The proposed approach uses an exterior penalty based cross-entropy (CE) method to solve the uni-level RBDO problem. This approach is shown to be robust in handling equality constraints. The three example problems solved in this paper also shows that the algorithm works well with different starting points used for the design variables.
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Rice, Andrew T., and Perry Y. Li. "Optimal Efficiency-Power Tradeoff for an Air Motor/Compressor With Volume Varying Heat Transfer Capability." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-6076.

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This paper presents the pressure-volume trajectories that yield the optimal tradeoff between efficiency and power during the compression and expansion of air. These results could benefit applications such as compressed air energy storage where both high efficiency and power density are required. Earlier work established solutions for the simple case in which hA, the product of the heat transfer coefficient and heat transfer surface area, is constant. This paper extends that analysis by allowing hA to vary with air volume. Solutions to the constrained, non-linear optimization problem are developed utilizing the method of Lagrange multipliers and Karush-Kuhn-Tucker (KKT) conditions. It is found that the optimal trajectory takes the form “fast-slow-fast” where the fast stages are adiabatic and the temperature change during the slow stage is proportional to the inverse root of the hA product. A case study predicts a 60% improvement in power over the constant-hA solution when both trajectories are run at 90% efficiency and hA = hA(V). Compared to linear- and sinusoidal-shaped trajectories, also at 90% efficiency, power gains are expected to be in the range of 500–1500%.
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Liang, Jinghong, Zissimos P. Mourelatos, and Jian Tu. "A Single-Loop Method for Reliability-Based Design Optimization." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57255.

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Reliability-Based Design Optimization (RBDO) can provide optimum designs in the presence of uncertainty. It can therefore, be a powerful tool for design under uncertainty. The traditional, double-loop RBDO algorithm requires nested optimization loops, where the design optimization (outer) loop, repeatedly calls a series of reliability (inner) loops. Due to the nested optimization loops, the computational effort can be prohibitive for practical problems. A single-loop RBDO algorithm is proposed in this paper for both normal and non-normal random variables. Its accuracy is the same with the double-loop approach and its efficiency is almost equivalent to deterministic optimization. It collapses the nested optimization loops into an equivalent single-loop optimization process by imposing the Karush-Kuhn-Tucker optimality conditions of the reliability loops as equivalent deterministic equality constraints of the design optimization loop. It therefore, converts the probabilistic optimization problem into an equivalent deterministic optimization problem, eliminating the need for calculating the Most Probable Point (MPP) in repeated reliability assessments. Several numerical applications including an automotive vehicle side impact example, demonstrate the accuracy and superior efficiency of the proposed single-loop RBDO algorithm.
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Xu, Meng, Georges Fadel, and Margaret M. Wiecek. "Dual Residual for Distributed Augmented Lagrangian Coordination Based on Optimality Conditions." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47002.

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Augmented Lagrangian Coordination (ALC) is one of the more popular coordination strategies for decomposition based optimization. It employs the augmented Lagrangian relaxation approach and has shown great improvements in terms of efficiency and solution accuracy when compared to other methods addressing the same type of problem. Additionally, by offering two variants: the centralized ALC in which an artificial master problem in the upper level is created to coordinate all the sub-problems in the lower level, and the distributed ALC in which coordination can be performed directly between sub-problems without a master problem, ALC provides more flexibility than other methods. However, the initial setting and the update strategy of the penalty weights in ALC still significantly affect its performance and thus are worth further research. For centralized ALC, the non-monotone weight update strategy based on the theory of dual residual has shown very good improvements over the traditional monotone update, in which the penalty weights can either increase or decrease. In this paper, we extend the research on the dual residual in centralized ALC to the distributed ALC. Through applying the Karush-Kuhn-Tucker (KKT) optimality conditions to the All-In-One (AIO) and decomposed problems, the necessary conditions for the decomposed solution to be optimal are derived, which leads to the definition of primal and dual residuals in distributed ALC. A new non-monotone weight based on both residuals is then proposed, by which all AIO KKT conditions are guaranteed after decomposition. Numerical tests are conducted on two mathematical problems and one engineering problem and the performances of the new update are compared to those of the traditional update. The results show that our proposed methods improve the process efficiency, accuracy, and robustness for distributed ALC.
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