Note: An algorithm to solve polyhedral convex set optimization problems
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SubjectSet-valued optimization; Set relations; set criterion; Vector optimization; infimum attainment
We provide a counterexample to the remark in Lohne 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.
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