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Discrete Optimization I

Discrete programmering. --- Optimaliseren. --- Mathematical optimization. --- Optimisation mathématique --- Mathematical optimization --- 519.85 --- 681.3*F22 --- 681.3*G16 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical programming --- Nonnumerical algorithms and problems: complexity of proof procedures; computations on discrete structures; geometrical problems and computations; pattern matching --See also {?681.3*E2-5}; {681.3*G2}; {?681.3*H2-3} --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*F22 Nonnumerical algorithms and problems: complexity of proof procedures; computations on discrete structures; geometrical problems and computations; pattern matching --See also {?681.3*E2-5}; {681.3*G2}; {?681.3*H2-3} --- 519.85 Mathematical programming --- Operational research. Game theory --- Mathematical analysis. --- 517.1 Mathematical analysis --- Programmation mathematique --- Colloque

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Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.

Algebra, Boolean --- Algebraic functions --- Functions, Algebraic --- Boolean algebra --- Boole's algebra --- Functions --- Algebraic logic --- Set theory --- Algebraic functions. --- Algebra, Boolean.

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Algebra, Boolean --- Operations research --- Algèbre de Boole --- Recherche opérationnelle

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Recherche opérationnelle --- Fonctions booléennes --- Graphes, Théorie des --- Programmation mathematique --- Programmation entiere

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Mathematical optimization.