This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.
Convex Analysis: Linear Spaces.- Maps on Linear Spaces.- Some Fundamental Theorems.- Theory of Vector Optimization: Optimality Notions.- Scalarization.- Existence Theorems.- Generalized Lagrange Multiplier Rule.- Duality.- Mathematical Applications: Vector Approximation.- Cooperative n Player Differential Games.- Engineering Applications: Theoretical Basics of Multiobjective Optimization.- Numerical Methods.- Multiobjective Design Problems.- Extensions to Set Optimization: Basic Concepts and Results of Set Optimization.- Contingent Epiderivatives.- Subdifferential.- Optimality Conditions.