Weijun Xie

Best Principal Submatrix Selection for the Maximum Entropy Sampling Problem: Scalable Algorithms and Performance Guarantees

  • Yongchun Li
  • Weijun Xie
    • Categories Data-Mining

    This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix with a given size out of a covariance matrix from a system. MESP has been widely applied to many areas, including healthcare, power system, manufacturing, data science, etc. Investigating its Lagrangian dual and primal characterization, we … Read more

    On the Cluster-aware Supervised Learning (CluSL): Frameworks, Convergent Algorithms, and Applications

  • Shutong Chen
  • Weijun Xie
    • Categories Data-Mining Tags , , , , ,

    This paper proposes a cluster-aware supervised learning (CluSL) framework, which integrates the clustering analysis with supervised learning (SL). The objective of CluSL is to simultaneously find the best clusters of the data points and minimize the sum of loss functions within each cluster. This framework has many potential applications in healthcare, operations management, manufacturing, and … Read more

    Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with $\infty- Distance

  • Weijun Xie
    • Categories Stochastic Programming Tags , , , ,

    In the optimization under uncertainty, decision-makers first select a wait-and-see policy before any realization of uncertainty and then place a here-and-now decision after the uncertainty has been observed. Two-stage stochastic programming is a popular modeling paradigm for the optimization under uncertainty that the decision-makers first specifies a probability distribution, and then seek the best decisions … Read more

    Sharing the Value-at-Risk under Distributional Ambiguity

  • Weijun Xie
  • Zhi Chen
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more

    Robust Multi-product Newsvendor Model with Substitution under Cardinality-constrained Uncertainty Set

  • Jie Zhang
  • Weijun Xie
  • Subhash Sarin
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where the demand and the substitution rates are stochastic and are subject to cardinality-constrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worst-case total profit. To achieve this, we first show that … Read more

    On Distributionally Robust Chance Constrained Programs with Wasserstein Distance

  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming

    This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and … Read more

    Scalable Algorithms for the Sparse Ridge Regression

  • Xinwei Deng
  • Weijun Xie
    • Categories Approximation Algorithms, Data-Mining, Integer Programming Tags , , , ,

    Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. This work focuses on sparse ridge regression, which enforces the sparsity by use of the L0 norm. We first prove that the continuous relaxation of the mixed integer second order conic (MISOC) reformulation using perspective formulation is equivalent to … Read more

    Multi-Product Newsvendor Problem with Customer-driven Demand Substitution: A Stochastic Integer Program Perspective

  • Jie Zhang
  • Weijun Xie
  • Subhash Sarin
    • Categories Applications - OR and Management Sciences Tags , , , ,

    This paper studies a multi-product newsvendor problem with customer-driven demand substitution, where each product, once run out of stock, can be proportionally substituted by the others. This problem has been widely studied in the literature, however, due to nonconvexity and intractability, only limited analytical properties have been reported and no efficient approaches have been proposed. … Read more

    Approximation Algorithms for D-optimal Design

  • Mohit Singh
  • Weijun Xie
    • Categories Combinatorial Optimization

    Experimental design is a classical statistics problem and its aim is to estimate an unknown m-dimensional vector from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental design problem, the goal is to pick k out of the given n experiments so as to make the most accurate estimate … Read more

    Bicriteria Approximation of Chance Constrained Covering Problems

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Combinatorial Optimization, Robust Optimization, Stochastic Programming

    A chance constrained optimization problem involves constraints with random data which can be violated with probability bounded above by a prespecified small risk parameter. Such constraints are used to model reliability requirements in a variety of application areas such as finance, energy, service and manufacturing. Except under very special conditions, chance constrained problems are extremely … Read more