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论文类型：期刊论文

发表时间：2017-01-01

发表刊物：17th British-French-German Conference on Optimization

收录刊物：SCIE、CPCI-S

卷号：32

期号：4,SI

页面范围：770-789

ISSN号：1055-6788

关键字：second-order dominance; probability discretization; Kantorovich metric; stabilityanalysis

摘要：Since the pioneering work by Dentcheva and Ruszczyski [Optimization with stochastic dominance constraints, SIAM J. Optim. 14 (2003), pp. 548-566], stochastic programs with second-order dominance constraints (SPSODC) have received extensive discussions over the past decade from theory of optimality to numerical schemes and practical applications. In this paper, we investigate discrete approximation of SPSODC when (a) the true probability is known but continuously distributed and (b) the true probability distribution is unknown but it lies within an ambiguity set of distributions. Differing from the well-known Monte Carlo discretization method, we propose a deterministic discrete approximation scheme due to Pflug and Pichler [Approximations for Probability Distributions and Stochastic Optimization Problems, International Series in Operations Research & Management Science, Vol. 163, Springer, New York, 2011, pp. 343-387] and demonstrate that the discrete probability measure and the ambiguity set of discrete probability measures approximate their continuous counterparts under the Kantorovich metric. Stability analysis of the optimal value and optimal solutions of the resulting discrete optimization problems is presented and some comparative numerical test results are reported.