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This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. All chapters are supplemented by thought-provoking problems. A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering. "Mathematicians wishing a self-contained introduction need look no further."& American Mathematical Monthly. 1982 ed.

Discrete mathematics --- Mathematical optimization --- Combinatorial optimization --- Computational complexity. --- Optimisation mathématique --- Optimisation combinatoire --- Complexité de calcul (Informatique) --- Computational Complexity --- Mathematical optimization. --- Combinatorial optimization. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Optimization, Combinatorial --- Combinatorial analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Optimisation mathématique --- Complexité de calcul (Informatique) --- Computational complexity

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Algorithms --- Linear programming --- Mathematical optimization --- 519.85 --- 519.85 Mathematical programming --- Mathematical programming --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Matrices --- Production scheduling --- Programming (Mathematics) --- Substitutions, Linear --- Transformations (Mathematics) --- Vector analysis --- Algorism --- Algebra --- Arithmetic --- Foundations --- Interior-point methods. --- Interior-point methods --- Linear programming. --- Linear Programming --- Algorithms. --- Mathematical optimization.

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Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.

Multiple criteria decision making. --- Nonlinear programming --- Operations research. --- Decision making. --- Mathematical optimization. --- Calculus of variations. --- Operations Research/Decision Theory. --- Optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making

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Integer programming --- Combinatorial optimization --- Congresses --- Computer science. --- Algorithms. --- Computer science --- Calculus of variations. --- Combinatorics. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematics. --- Programming (Mathematics) --- Computer software. --- Computational complexity. --- Mathematical optimization. --- Combinatorics --- Algebra --- Mathematical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Complexity, Computational --- Electronic data processing --- Machine theory --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Algorism --- Arithmetic --- Foundations --- Integer programming - Congresses --- Combinatorial optimization - Congresses

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During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.

Algorithmes (Ordinateur) --- Algoritmen (Computer) --- Approximatietheorie --- Approximation theory --- Automatic theorem proving --- Computer algorithms --- Theorema's--Automatische bewijsvoering --- Théorie des approximations --- Théorèmes--Démonstration automatique --- Computer Science --- Engineering & Applied Sciences --- Theory of approximation --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Computer science. --- Computers. --- Algorithms. --- Computer science --- Calculus of variations. --- Combinatorics. --- Computer Science. --- Theory of Computation. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Computation by Abstract Devices. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematics. --- Information theory. --- Computer software. --- Computational complexity. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Complexity, Computational --- Electronic data processing --- Machine theory --- Software, Computer --- Computer systems --- Communication theory --- Communication --- Cybernetics --- Combinatorics --- Algebra --- Informatics --- Science --- Computer science—Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Algorism --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Calculators --- Cyberspace --- Foundations