Set optimization - a rather short introduction

Abstract

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems.

References in corpus (2)

• Directional derivatives and subdifferentials of set-valued convex functions
• A Minty variational principle for set optimization

Cited by in corpus (12)

• Dual representations for systemic risk measures
• Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations
• Set Relations and Approximate Solutions in Set Optimization
• The Fermat Rule for Set Optimization Problems with Lipschitzian Set-Valued Mappings
• Existence of solutions for polyhedral convex set optimization problems
• Set-Valued Backward Stochastic Differential Equations
• Euler-Lagrange equations for multiobjective calculus of variations problems via set optimization
• The inf-translation for solving set minimization problems
• On unbounded polyhedral convex set optimization problems
• Approximate Vertex Enumeration
• Multistage Portfolio Optimization: A Duality Result in Conic Market Models
• A set optimization approach to zero-sum matrix games with multi-dimensional payoffs