Sanjay Mehrotra

A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization

  • Sanjay Mehrotra
  • Dávid Papp
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming Tags , , , , , , ,

    We first present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with non-differentiable semi-infinite … Read more

    Generating moment matching scenarios using optimization techniques

  • Sanjay Mehrotra
  • Dávid Papp
    • Categories Stochastic Programming Tags , ,

    An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the … Read more

    Robust Decision Making using a General Utility Set

  • Manish Bansal
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

    We develop the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. A robust decision-making framework is built on a utility set which characterizes a decision maker’s risk attitude described by boundary and auxiliary conditions. This framework is studied using the Sample Average Approximation (SAA) approach. We show the … Read more

    Solution of monotone complementarity and general convex programming problems using modified potential reduction interior point method

  • Kuo-Ling Huang
  • Sanjay Mehrotra
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Quadratic Programming Tags , , , ,

    We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition is satis ed. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation … Read more

    Robust Decision Making using a Risk-Averse Utility Set

  • Jian Hu
  • Sanjay Mehrotra
    • Categories Applications - OR and Management Sciences, Finance and Economics, Robust Optimization Tags , , , ,

    Eliciting the utility of a decision maker is difficult. In this paper, we develop a flexible decision making framework, which uses the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. The ideas are developed by giving a probabilistic interpretation to utility and marginal utility functions. Boundary and additional … Read more

    Concepts and Applications of Stochastically Weighted Stochastic Dominance

  • Tito Homem-de-Mello
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Stochastic Programming Tags , , , ,

    Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multi-criterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts … Read more

    Models and Algorithms for Distributionally Robust Least Squares Problems

  • Sanjay Mehrotra
  • He Zhang
    • Categories Robust Optimization, Second-Order Cone Programming, Semi-definite Programming Tags , ,

    We present different robust frameworks using probabilistic ambiguity descriptions of the input data in the least squares problems. The three probability ambiguity descriptions are given by: (1) confidence interval over the first two moments; (2) bounds on the probability measure with moments constraints; (3) confidence interval over the probability measure by using the Kantorovich probability … Read more

    Robust and Stochastically Weighted Multi-Objective Optimization Models and Reformulations

  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more

    An Empirical Evaluation of Walk-and-Round Heuristics for Mixed-Integer Linear Programs

  • Kuo-Ling Huang
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Linear Programming Tags , , , ,

    Geometric random walks have been proposed and analyzed for solving optimization problems. In this paper we report our computational experience with generating feasible integer solutions of mixed-integer linear programs using geometric random walks, and a random ray approach. A feasibility pump is used to heuristically round the generated points. Computational results on MIPLIB2003 and COR@L … Read more

    Risk Adjusted Budget Allocation Models with Application in Homeland Security

  • Tito Homem-de-Mello
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , , , ,

    This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more