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Convex functions --- Convex sets --- 514.17 --- Convex sets. Geometric figure arrangements. Geometric inequalities --- 514.17 Convex sets. Geometric figure arrangements. Geometric inequalities --- Convexe functies --- Convexe verzamelingen --- Ensembles convexes --- Sets [Convex ] --- Sets, Convex --- Functions, Convex --- Analyse convexe --- Langages de programmation --- Recherche opérationnelle --- Programmation

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514.17 --- Convex sets --- Sets, Convex --- Convex domains --- Set theory --- Convex sets. Geometric figure arrangements. Geometric inequalities --- Convex sets. --- 514.17 Convex sets. Geometric figure arrangements. Geometric inequalities --- Convex geometry. --- Géométrie convexe. --- Duality theory (Mathematics) --- Dualité, Principe de (mathématiques) --- Polytopes

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This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

Convex sets. --- Fourier series. --- Spherical harmonics. --- Functions, Potential --- Potential functions --- Harmonic analysis --- Harmonic functions --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Sets, Convex --- Convex domains --- Set theory

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This book develops the concepts of fundamental convex analysis and optimization by using advanced calculus and real analysis. Brief accounts of advanced calculus and real analysis are included within the book. The emphasis is on building a geometric intuition for the subject, which is aided further by supporting figures. Two distinguishing features of this book are the use of elementary alternative proofs of many results and an eclectic collection of useful concepts from optimization and convexity often needed by researchers in optimization, game theory, control theory, and mathematical economics. A full chapter on optimization algorithms gives an overview of the field, touching upon many current themes. The book is useful to advanced undergraduate and graduate students as well as researchers in the fields mentioned above and in various engineering disciplines.

Convex sets. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Sets, Convex --- Convex domains --- Set theory --- Optimization. --- Conjunts convexos --- Optimització matemàtica

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517.51 --- Functions of a real variable. Real functions --- Convex functions. --- Convex sets. --- Convex programming. --- 517.51 Functions of a real variable. Real functions --- Convex functions --- Convex programming --- Convex sets --- Sets, Convex --- Convex domains --- Set theory --- Programming (Mathematics) --- Functions, Convex --- Functions of real variables --- Convex geometry. --- Géométrie convexe. --- Fonctions convexes. --- Géometrie convexe --- Analyse convexe --- Programmation mathematique --- Programmation convexe