An algorithm to solve polyhedral convex set optimization problems

DOI10.1080/02331934.2012.749259zbMath1292.90271arXiv1210.0729OpenAlexW2952908520MaRDI QIDQ4916312

Andreas Löhne, Carola Schrage

Publication date: 22 April 2013

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0729

zbMATH Keywords

vector optimizationset-valued optimizationset relationset criterioninfimum attainment

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29)

Related Items (13)

Solving set-valued optimization problems using a multiobjective approach ⋮ A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle ⋮ A Vectorization Scheme for Nonconvex Set Optimization Problems ⋮ An algorithmic approach to multiobjective optimization with decision uncertainty ⋮ Solving set optimization problems based on the concept of null set ⋮ Lagrange duality in set optimization ⋮ Set Optimization—A Rather Short Introduction ⋮ A Survey of Set Optimization Problems with Set Solutions ⋮ Note: An algorithm to solve polyhedral convex set optimization problems ⋮ Benson type algorithms for linear vector optimization and applications ⋮ Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization ⋮ A derivative-free descent method in set optimization ⋮ Vectorization in set optimization

Uses Software

• BENSOLVE

Cites Work

• A dual variant of Benson's ``outer approximation algorithm for multiple objective linear programming
• New order relations in set optimization
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• Further analysis of an outcome set-based algorithm for multiple-objective linear programming
• Primal-dual methods for vertex and facet enumeration
• Variational methods in partially ordered spaces
• Set-valued risk measures for conical market models
• Vector Optimization with Infimum and Supremum
• Solution concepts in vector optimization: a fresh look at an old story
• Duality in Vector Optimization
• Duality for Set-Valued Measures of Risk
• The quickhull algorithm for convex hulls
• A new approach to duality in vector optimization

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