Fixed Point Theory, Variational Analysis, and Optimization

This book not only covers 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. Packed with detailed proofs, the text supplies an introduction to the field and a guideline to the literature, progressing from basic concepts to the latest developments. It provides fundamental knowledge of directional derivatives and monotonicity required in understanding and solving variational inequality problems.

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

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.