Zhiping Chen

Distributionally robust second-order stochastic dominance constrained optimization with Wasserstein distance

  • Zhiping Chen
  • Jia Liu
  • Yu Mei
    • Categories Robust Optimization

    We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the empirical distribution. We adopt the sample approximation approach to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition … Read more

    Rates of convergence of sample average approximation under heavy tailed distributions

  • Zhiping Chen
  • Jie Jiang
  • Xinmin Yang
    • Categories Stochastic Programming

    In this paper, we consider the rate of convergence with sample average approximation (SAA) under heavy tailed distributions and quantify it under both independent identically distributed (iid) sampling and non-iid sampling. We rst derive the polynomial rate of convergence for random variable under iid sampling. Then, the uniform polynomial rates of convergence for both random … Read more

    Distributionally robust chance constrained geometric optimization

  • Jia Liu
  • Abdel Lisser
  • Zhiping Chen
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    This paper discusses distributionally robust geometric programs with individual and joint chance constraints. Seven groups of uncertainty sets are considered: uncertainty sets with first two order moments information, uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution or a discrete reference distribution, uncertainty sets with known first moments or known first … Read more

    Quantitative Stability of Two-stage Stochastic Linear Programs with Full Random Recourse

  • Zhiping Chen
  • Jie Jiang
    • Categories Stochastic Programming

    In this paper, we use the parametric programming technique and pseudo metrics to study the quantitative stability of the two-stage stochastic linear programming problem with full random recourse. Under the simultaneous perturbation of the cost vector, coefficient matrix and right-hand side vector, we first establish the locally Lipschitz continuity of the optimal value function and … Read more

    Joint rectangular geometric chance constrained programs

  • Zhiping Chen
  • Abdel Lisser
  • Jia Liu
  • Chuan Xu
    • Categories Stochastic Programming Tags , , ,

    This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear approximation method. Our results show … Read more

    Scenario Tree Reduction Methods Through Changing Node Values

  • Zhiping Chen
  • Zhe Yan
    • Categories Stochastic Programming Tags , , ,

    To develop practical and efficient scenario tree reduction methods, we introduce a new methodology which allows for changing node values, and an easy-to-calculate distance function to measure the difference between two scenario trees. Based on minimizing the new distance, we first construct a primitive scenario tree reduction model which also minimizes the Wasserstein distance between … Read more

    Stochastic geometric optimization with joint probabilistic constraints

  • Zhiping Chen
  • Abdel Lisser
  • Jia Liu
    • Categories Stochastic Programming Tags , , ,

    This paper discusses geometric programs with joint probabilistic constraints. When the stochastic parameters are normally distributed and independent of each other, we approximate the problem by using piecewise polynomial functions with non-negative coefficients, and transform the approximation problem into a convex geometric program. We prove that this approximation method provides a lower bound. Then, we … Read more

    A directional distance based super-efficiency DEA model handling negative data

  • Zhiping Chen
  • Ruiyue Lin
    • Categories Applications - OR and Management Sciences

    This paper develops a new radial super-efficiency data envelopment analysis (DEA) model, which allows input-output variables to take both negative and positive values. Compared with existing DEA models capable of dealing with negative data, the proposed model can rank the efficient DMUs and is feasible no matter whether the input-output data are non-negative or not. … Read more

    Multi-period fund performance evaluation: A dynamic network DEA approach with diversification and the directional distance function

  • Zhiping Chen
  • Qianhui Hu
  • Ruiyue Lin
    • Categories Finance and Economics

    When analyzing the relative performance of mutual funds, current data envelopment analysis (DEA) models with diversification only consider risks and returns over the entire investment process, which ignore the performance change in consecutive periods. This paper introduces a novel multi-period network DEA approach with diversification and the directional distance function. The new approach decomposes the … Read more