Benson type algorithms for linear vector optimization and applications

DOI10.1007/s10898-013-0098-2zbMath1330.90099arXiv1302.2415OpenAlexW3100995391MaRDI QIDQ743969

Andreas H. Hamel, Birgit Rudloff, Andreas Löhne

Publication date: 2 October 2014

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2415

zbMATH Keywords

algorithmsvector optimizationlinear programmingdualityouter approximationtransaction costsmultiple objective optimizationset-valued risk measure

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Linear programming (90C05) Actuarial science and mathematical finance (91G99)

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Uses Software

• Qhull
• BENSOLVE

Cites Work

• Unnamed Item
• Set-valued average value at risk and its computation
• A dual variant of Benson's ``outer approximation algorithm for multiple objective linear programming
• On duality in multiple objective linear programming
• An approximation algorithm for convex multi-objective programming problems
• A duality theory for set-valued functions. I: Fenchel conjugation theory
• Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning
• Approximating the nondominated set of an MOLP by approximately solving its dual problem
• Set-valued duality theory for multiple objective linear programs and application to mathematical finance
• Further analysis of an outcome set-based algorithm for multiple-objective linear programming
• An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem
• Primal-dual methods for vertex and facet enumeration
• Vector-valued coherent risk measures
• Set-valued risk measures for conical market models
• Lagrange duality in set optimization
• Coherent Measures of Risk
• Geometric Duality for Convex Vector Optimization Problems
• Stochastic Finance
• Vector Optimization with Infimum and Supremum
• Solution concepts in vector optimization: a fresh look at an old story
• A Fenchel–Rockafellar duality theorem for set-valued optimization
• Duality for Set-Valued Measures of Risk
• Geometric Duality in Multiple Objective Linear Programming
• The decoupling approach to binomial pricing of multi-asset options
• The quickhull algorithm for convex hulls
• An algorithm to solve polyhedral convex set optimization problems
• AN ALGORITHM FOR CALCULATING THE SET OF SUPERHEDGING PORTFOLIOS IN MARKETS WITH TRANSACTION COSTS
• Frontiers of Stochastically Nondominated Portfolios