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Le but de cet ouvrage est de faire une présentation complète et auto contenue de l'équivalence entre les Oracles Séparer, Optimiser et Appartenir en Optimisation Polyédrale. Dans ce but le livre commence par une présentation détaillée des problèmes de Complexité des Algorithmes suivi d'une présentation de la méthode du Simplexe. On décrit ensuite l'algorithme de Khachiyan sans éluder les problèmes numériques. Viennent alors une suite d'algorithmes polynomiaux pour Optimiser à partir de l'oracle Séparer. Après quelques transformations, on montre que, par polarité, on peut Séparer à partir de l'oracle Optimiser. La première équivalence est revue après avoir décrit l'algorithme LLL. L'ouvrage se termine par la réduction de Séparer à Appartenir

Linear Programming --- Programming (Mathematics)

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Convex geometry. --- Functional analysis. --- Programming (Mathematics)

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Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated

Combinatorial optimization --- Mathematical optimization --- Nonlinear programming --- Programming (Mathematics)

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This solutions manual is a companion volume to the classic textbook Recursive Methods in Economic Dynamics by Nancy L. Stokey and Robert E. Lucas. Efficient and lucid in approach, this manual will greatly enhance the value of Recursive Methods as a text for self-study.

Economics, Mathematical --- Recursive Functions --- Dynamic programming --- Economics, Mathematical. --- Recursive functions. --- Dynamic programming. --- Recursive functions --- E-books --- Mathematical optimization --- Programming (Mathematics) --- Systems engineering --- Functions, Recursive --- Algorithms --- Arithmetic --- Logic, Symbolic and mathematical --- Number theory --- Recursion theory --- Decidability (Mathematical logic) --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Foundations --- Methodology --- Mathématiques économiques --- Récursivité, Théorie de la --- Économétrie --- Programmation dynamique --- Économie politique --- Modèles mathématiques

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Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.

Algorithms. --- Electronic books. -- local. --- Linear programming. --- Linear programming --- Algorithms --- Operations Research --- Calculus --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- 519.85 --- 681.3*G16 --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.85 Mathematical programming --- Mathematical programming --- Algorism --- Algebra --- Arithmetic --- Matrices --- Production scheduling --- Programming (Mathematics) --- Substitutions, Linear --- Transformations (Mathematics) --- Vector analysis --- Foundations --- Mathematics. --- Operations research. --- Decision making. --- Mathematical optimization. --- Calculus of variations. --- Management science. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization. --- Operations Research, Management Science. --- Operation Research/Decision Theory. --- Operations Research/Decision Theory. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Quantitative business analysis --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Simulation methods --- System analysis --- Isoperimetrical problems --- Variations, Calculus of --- Decision making