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Programming (Mathematics) --- Convex programming --- Interior-point methods --- #TELE:SISTA --- Convex programming. --- Interior-point methods. --- Programmation (mathématiques) --- Calcul des variations --- Programmation mathematique --- Programmation convexe

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Operational research. Game theory --- Convex programming --- Convex sets --- Convex functions --- 330.105 --- 519.8 --- Wiskundige economie. Wiskundige methoden in de economie --- Operational research --- Convex programming. --- Convex sets. --- Convex functions. --- 519.8 Operational research --- 330.105 Wiskundige economie. Wiskundige methoden in de economie --- Programmation mathematique --- Programmation convexe

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Analytical spaces --- Banach spaces. --- Hilbert space. --- Convex functions. --- Convex programming. --- Nonlinear functional analysis. --- Analyse fonctionnelle non linéaire. --- Mathematical optimization. --- Optimisation mathématique. --- Analyse convexe --- Programmation (mathématiques) --- Analyse fonctionnelle non linéaire --- Optimisation mathématique. --- Programmation (mathématiques)

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An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.

Banach spaces. --- Convex functions. --- Hilbert space. --- Mathematical optimization. --- Banach spaces --- Hilbert space --- Convex functions --- Convex programming --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Calculus --- Convex programming. --- Functions, Convex --- Mathematics. --- Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Programming (Mathematics) --- Functions of real variables --- Hyperspace --- Inner product spaces --- Functions of complex variables --- Generalized spaces --- Topology

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Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text. Applications benefiting from simplicial partitioning are examined in detail such as nonlinear least squares regression and pile placement optimization in grillage-type foundations. Researchers and engineers will benefit from simplicial partitioning algorithms such as Lipschitz branch and bound, Lipschitz optimization without the Lipschitz constant, heuristic partitioning presented. This book will leave readers inspired to develop simplicial versions of other algorithms for global optimization and even use other non-rectangular partitions for special applications.

Mathematics. --- Combinatorial analysis. --- Nonconvex programming. --- Global optimization --- Non-convex programming --- Combinatorics --- Math --- Applied mathematics. --- Engineering mathematics. --- Operations research. --- Management science. --- Combinatorics. --- Operations Research, Management Science. --- Applications of Mathematics. --- Programming (Mathematics) --- Algebra --- Mathematical analysis --- Science --- Engineering --- Engineering analysis --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics --- Mathematical optimization.