Note: An algorithm to solve polyhedral convex set optimization problems

Abstract

We provide a counterexample to the remark in Löhne and Schrage [An algorithm to solve polyhedral convex set optimization problems, Optimization 62 (2013), pp. 131-141] that every solution of a polyhedral convex set optimization problem is a pre-solution. A correct statement is that every solution of a polyhedral convex set optimization problem obtained by the algorithm SetOpt is a pre-solution. We also show that every finite infimizer and hence every solution of a polyhedral convex set optimization problem contains a pre-solution.

Keywords:

• set-valued optimization
• set relation
• set criterion
• vector optimization
• infimum attainment

AMS Subject Classifications:

• 65K05
• 90C99