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Full Description
Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis—fixed point theory, variational inequalities, and vector optimization—but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions involving differentiable or directionally differentiable functions. This essential reference supplies both an introduction to the field and a guideline to the literature, progressing from basic concepts to the latest developments. Packed with detailed proofs and bibliographies for further reading, the text:
Examines Mann-type iterations for nonlinear mappings on some classes of a metric space
Outlines recent research in fixed point theory in modular function spaces
Discusses key results on the existence of continuous approximations and selections for set-valued maps with an emphasis on the nonconvex case
Contains definitions, properties, and characterizations of convex, quasiconvex, and pseudoconvex functions, and of their strict counterparts
Discusses variational inequalities and variational-like inequalities and their applications
Gives an introduction to multi-objective optimization and optimality conditions
Explores multi-objective combinatorial optimization (MOCO) problems, or integer programs with multiple objectives
Fixed Point Theory, Variational Analysis, and Optimization is a beneficial resource for the research and study of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics. It provides fundamental knowledge of directional derivatives and monotonicity required in understanding and solving variational inequality problems.
Contents
Common Fixed Points in Convex Metric Spaces. Fixed Points of Nonlinear Semigroups in Modular Function Spaces. Approximation and Selection Methods for Set-Valued Maps and Fixed Point Theory. Convexity, Generalized Convexity, and Applications. New Developments in Quasiconvex Optimization. An Introduction to Variational-Like Inequalities. Vector Optimization: Basic Concepts and Solution Methods. Multi-Objective Combinatorial Optimization.
