Robust Optimization Approximation for Ambiguous P-Model and Its Application

Abstract

Robust optimization is a powerful and relatively novel methodology to cope with optimization problems in the presence of uncertainty. The positive aspect of robust optimization approach is its computational tractability that attracts more and more attention. In this paper, we focus on an ambiguous P-model where probability distributions are partially known. We discuss robust counterpart (RC) of uncertain linear constraints under two refined uncertain sets by robust approach and further find the safe tractable approximations of chance constraints in the ambiguous P-model. Because of the probability constraints embedded in the ambiguous P-model, it is computationally intractable. The advantage of our approach lies in choosing an implicit way to treat stochastic uncertainty models instead of solving them directly. The process above can enable the transformation of proposed P-model to a tractable deterministic one under the refined uncertainty sets. A numerical example about portfolio selection demonstrates that the ambiguous P-model can help the decision maker to determine the optimal investment proportions of various stocks. Sensitivity analyses explore the trade-off between optimization and robustness by adjusting parameter values. Comparison study is conducted to validate the benefit of our ambiguous P-model.

Optimizing sustainable development problem under uncertainty: Robust vs fuzzy optimization methods

“…Ben-Tal and Newmirovsky [7,8] successively proved that the robust convex formulation of programming problems with uncertainty is tractable when the uncertainty set is described as a box or an ellipsoid. An extension of this method can be referred to the literature [9,10,20]. For a thorough coverage of developments and recent advances in robust optimization, the interested reader can refer to [13].…”