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
CONTENT
Convex Analysis and Set-Valued Maps: A Review -- Asymptotic Cones and Functions -- Existence and Stability in Optimization Problems -- Minimizing and Stationary Sequences -- Duality in Optimization Problems -- Maximal Monotone Maps and Variational Inequalities
Mathematics
Mathematical analysis
Analysis (Mathematics)
Potential theory (Mathematics)
Mathematical models
Mathematical optimization
Calculus of variations
Operations research
Management science
Mathematics
Mathematical Modeling and Industrial Mathematics
Analysis
Potential Theory
Calculus of Variations and Optimal Control; Optimization
