Xiaojin Zheng

An Alternating Direction Method for Chance-Constrained Optimization Problems with Discrete Distributions

  • Xiaodi Bai
  • Jie Sun
  • Xiaoling Sun
  • Xiaojin Zheng
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Stochastic Programming

    We consider a chance-constrained optimization problem (CCOP), where the random variables follow finite discrete distributions. The problem is in general nonconvex and can be reformulated as a mixed-integer program. By exploiting the special structure of the probabilistic constraint, we propose an alternating direction method for finding suboptimal solutions of CCOP. At each iteration, this method … Read more

    Successive Convex Approximations to Cardinality-Constrained Quadratic Programs: A DC Approach

  • Duan Li
  • Jie Sun
  • Xiaoling Sun
  • Xiaojin Zheng
    • Categories Global Optimization, Integer Programming, Nonlinear Optimization

    In this paper we consider a cardinality-constrained quadratic program that minimizes a convex quadratic function subject to a cardinality constraint and linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality … Read more

    Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach

  • Duan Li
  • Xiaoling Sun
  • Xiaojin Zheng
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Semi-definite Programming

    We consider in this paper quadratic programming problems with cardinality and minimum threshold constraints which arise naturally in various real-world applications such as portfolio selection and subset selection in regression. We propose a new semidefinite program (SDP) approach for computing the “best” diagonal decomposition that gives the tightest continuous relaxation of the perspective reformulation. We … Read more