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This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.
Convex domains. --- Mathematics. --- Algebra. --- Field theory (Physics). --- Group theory. --- Mathematical analysis. --- Analysis (Mathematics). --- Convex geometry. --- Discrete geometry. --- Convex and Discrete Geometry. --- Analysis. --- Field Theory and Polynomials. --- Group Theory and Generalizations. --- Geometry --- Combinatorial geometry --- 517.1 Mathematical analysis --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Math --- Science --- Convex regions --- Convexity --- Calculus of variations --- Convex geometry --- Point set theory --- Discrete groups. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Algebraic fields. --- Polynomials. --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra)
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Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business. .
Integer programming. --- Linear programming. --- Convex domains. --- Convex regions --- Convexity --- Calculus of variations --- Convex geometry --- Point set theory --- Production scheduling --- Programming (Mathematics) --- Matrix theory. --- Mathematics. --- Algorithms. --- Combinatorics. --- Mathematical optimization. --- Operations research. --- Linear and Multilinear Algebras, Matrix Theory. --- Game Theory, Economics, Social and Behav. Sciences. --- Optimization. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Combinatorics --- Algebra --- Algorism --- Arithmetic --- Math --- Science --- Foundations --- Algebra. --- Game theory. --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Decision making
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