Set Optimization—A Rather Short Introduction

DOI10.1007/978-3-662-48670-2_3zbMath1337.49001arXiv1404.5928OpenAlexW1574443838MaRDI QIDQ2805754

Andreas H. Hamel, Carola Schrage, Birgit Rudloff, Frank Heyde, Andreas Löhne

Publication date: 13 May 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.5928

zbMATH Keywords

vector optimizationset-valued functionsdualitysubdifferentialscalarizationrisk measureBenson's algorithmset optimizationset relationconlinear spaceinfimizer

Mathematics Subject Classification ID

Related Items (35)

Time Consistency of the Mean-Risk Problem ⋮ Applying set optimization to weak efficiency ⋮ On the ordinal structure of the weighted set relation ⋮ A set optimization approach to zero-sum matrix games with multi-dimensional payoffs ⋮ Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior ⋮ Set-valued dynamic risk measures for processes and for vectors ⋮ Optimality conditions for set-valued optimisation problems using a modified Demyanov difference ⋮ Cone distribution functions and quantiles for multivariate random variables ⋮ Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets ⋮ Vector optimization with domination structures: variational principles and applications ⋮ A topological convergence on power sets well-suited for set optimization ⋮ Further characterizations of possibility-theoretical indices in fuzzy optimization ⋮ Conjugate duality in set optimization via nonlinear scalarization ⋮ A set optimization approach to utility maximization under transaction costs ⋮ Hadamard well-posedness and stability in set optimization ⋮ Characteristic curves for set-valued Hamilton-Jacobi equations ⋮ On global well-posedness of semi-infinite set optimization problems ⋮ Lower Cone Distribution Functions and Set-Valued Quantiles Form Galois Connections ⋮ A supermartingale relation for multivariate risk measures ⋮ Tractability of convex vector optimization problems in the sense of polyhedral approximations ⋮ The value functions approach and Hopf-Lax formula for multiobjective costs via set optimization ⋮ On robustness for set-valued optimization problems ⋮ Multi-utility representations of incomplete preferences induced by set-valued risk measures ⋮ Dual representations for systemic risk measures ⋮ Editorial. Choosing sets: preface to the special issue on set optimization and applications ⋮ Multi-criteria decision making via multivariate quantiles ⋮ Ekeland's variational principle with weighted set order relations ⋮ A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa's set approach ⋮ CAPITAL ALLOCATION FOR SET-VALUED RISK MEASURES ⋮ Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization ⋮ Minimal element theorems revisited ⋮ Approximate solutions and Levitin-Polyak well-posedness for set optimization using weak efficiency ⋮ Global Well-Posedness in Set Optimization ⋮ The Hopf-Lax formula for multiobjective costs with non-constant discount via set optimization ⋮ A characterization theorem for Aumann integrals

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