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Nonlinear applied analysis and in particular the related ?elds of continuous optimization and variational inequality problems have gone through major developments over the last three decades and have reached maturity. A pivotal role in these developments has been played by convex analysis, a rich area covering a broad range of problems in mathematical sciences and its applications. Separation of convex sets and the Legendre–Fenchel conjugate transforms are fundamental notions that have laid the ground for these fruitful developments. Two other fundamental notions that have contributed to making convex analysis a powerful analytical tool and that haveoftenbeenhiddeninthesedevelopmentsarethenotionsofasymptotic sets and functions. The purpose of this book is to provide a systematic and comprehensive account of asymptotic sets and functions, from which a broad and u- ful theory emerges in the areas of optimization and variational inequa- ties. There is a variety of motivations that led mathematicians to study questions revolving around attaintment of the in?mum in a minimization problem and its stability, duality and minmax theorems, convexi?cation of sets and functions, and maximal monotone maps. In all these topics we are faced with the central problem of handling unbounded situations.

Convex functions. --- Convex programming. --- Mathematical optimization. --- Variational inequalities (Mathematics) --- Global analysis (Mathematics). --- Potential theory (Mathematics). --- Mathematical Modeling and Industrial Mathematics. --- Analysis. --- Potential Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization. --- Operations Research, Management Science. --- Mathematical models. --- Mathematical analysis. --- Analysis (Mathematics). --- Calculus of variations. --- Operations research. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- 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 --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mechanics --- 517.1 Mathematical analysis --- Models, Mathematical --- Functions, Convex --- Functions of real variables --- Programming (Mathematics) --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities