Dali Zhang

Data-Driven Distributionally Preference Robust Optimization Models Based on Random Utility Representation in Multi-Attribute Decision Making

  • Jian Hu
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more

    Convergence Analysis and a DC Approximation Method for Data-driven Mathematical Programs with Distributionally Robust Chance Constraints

  • Hailin Sun
  • Chen Yannan
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    In this paper, we consider the convergence analysis of data-driven mathematical programs with distributionally robust chance constraints (MPDRCC) under weaker conditions without continuity assumption of distributionally robust probability functions. Moreover, combining with the data-driven approximation, we propose a DC approximation method to MPDRCC without some special tractable structures. We also give the convergence analysis of … Read more

    Confidence Levels for CVaR Risk Measures and Minimax Limits

  • Edward Anderson
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming

    Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and its … Read more

    Stochastic Nash Equilibrium Problems: Sample Average Approximation and Applications

  • Huifu Xu
  • Dali Zhang
    • Categories Game Theory, Nonsmooth Optimization, Stochastic Programming Tags , , ,

    This paper presents a Nash equilibrium model where the underlying objective functions involve uncertainty and nonsmoothness. The well known sample average approximation method is applied to solve the problem and the first order equilibrium conditions are characterized in terms of Clarke generalized gradients. Under some moderate conditions, it is shown that with probability one, a … Read more

    A Two Stage Stochastic Equilibrium Model for Electricity Markets with Two Way Contracts

  • Yue Wu
  • Huifu Xu
  • Dali Zhang
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities

    This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans, … Read more