A derivative-free descent method in set optimization

Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical method for the determination of optimal scenarios is presented. A new derivative-free descent method for the solution of set optimization problems is given together with numerical results in low dimensions. Copyright Springer Science+Business Media New York 2015