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Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization.  With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields. .

Mathematics. --- Mathematical optimization. --- Optimization. --- Classical Mechanics. --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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Stochastic programming. --- Mathematical optimization. --- Numbers, Random. --- Random numbers --- Random sampling numbers --- Random data (Statistics) --- Sampling (Statistics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Linear programming

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This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.

Mathematical optimization. --- Evolutionary computation. --- Computation, Evolutionary --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematics. --- Calculus of variations. --- Engineering design. --- Discrete Optimization. --- Continuous Optimization. --- Engineering Design. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Neural networks (Computer science) --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Design --- Isoperimetrical problems --- Variations, Calculus of

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Ce livre considère le traitement de problèmes d'optimisation de grande taille. L'idée est d'éclater le problème d'optimisation global en sous-problèmes plus petits, donc plus faciles à résoudre, chacun impliquant l'un des sous-systèmes (décomposition), mais sans renoncer à obtenir l'optimum global, ce qui nécessite d'utiliser une procédure itérative (coordination). Ce sujet a fait l'objet de plusieurs livres publiés dans les années 70 dans le contexte de l'optimisation déterministe. Nous présentans ici les principes essentiels et méthodes de décomposition-coordination au travers de situations typiques, puis nous proposons un cadre général qui permet de construire des algorithmes corrects et d'étudier leur convergence. Cette théorie est présentée aussi bien dans le contexte de l'optimisation déterministe que stochastique. Ce matériel a été enseigné par les auteurs dans divers cours de 3ème cycle et également mis en œuvre dans de nombreuses applications industrielles. Des exercices et problèmes avec corrigés illustrent le potentiel de cette approche. Decomposition-coordination in deterministic and stochastic optimization This book discusses large-scale optimization problems involving systems made up of interconnected subsystems. The main viewpoint is to break down the overall optimization problem into smaller, easier-to-solve subproblems, each involving one subsystem (decomposition), without sacrificing the objective of achieving the global optimum, which requires an iterative process (coordination). This topic emerged in the 70’s in the context of deterministic optimization. The present book describes the main principles and methods of decomposition-coordination using typical situations, then proposes a general framework that makes it possible to construct well-behaved algorithms and to study their convergence. This theory is presented in the context of deterministic as well as stochastic optimization, and has been taught by the authors in graduate courses and implemented in numerous industrial applications. The book also provides exercises and problems with answers to illustrate the potential of this approach.

Mathematics. --- Algorithms. --- Mathematical optimization. --- Probabilities. --- Optimization. --- Probability Theory and Stochastic Processes. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algorism --- Algebra --- Arithmetic --- Foundations --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk