Benson type algorithms for linear vector optimization and applications

Abstract

New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new set-valued risk measure for multivariate positions.

References in corpus (1)

• An Algorithm to Solve Polyhedral Convex Set Optimization Problems

Cited by in corpus (9)

• Set optimization - a rather short introduction
• The vector linear program solver Bensolve -- notes on theoretical background
• Set-valued shortfall and divergence risk measures
• A Parametric Simplex Algorithm for Linear Vector Optimization Problems
• A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle
• A vector linear programming approach for certain global optimization problems
• Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations
• Enhancing Branch-and-Bound for Multi-Objective 0-1 Programming
• A Benson-Type Algorithm for Bounded Convex Vector Optimization Problems with Vertex Selection