Karthik Natarajan

On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems

  • Samuel Burer
  • Karthik Natarajan
    • Categories Quadratic Programming, Robust Optimization, Semi-definite Programming Tags , ,

    We show that continuous quadratic submodular minimization with bounds is solvable in polynomial time using semidefinite programming, and we apply this result to two moment problems arising in distributionally robust optimization and the computation of covariance bounds. Accordingly, this research advances the ongoing study of continuous submodular minimization and opens new application areas therein. ArticleDownload … Read more

    Distributionally robust optimization through the lens of submodularity

  • Karthik Natarajan
  • Divya Padmanabhan
  • Arjun Ramachandra
    • Categories Convex Optimization, Linear Programming, Linear, Cone and Semidefinite Programming Tags , , , ,

    Distributionally robust optimization is used to solve decision making problems under adversarial uncertainty where the distribution of the uncertainty is itself ambiguous. In this paper, we identify a class of these instances that is solvable in polynomial time by viewing it through the lens of submodularity. We show that the sharpest upper bound on the … Read more

    Discrete Optimal Transport with Independent Marginals is #P-Hard

  • Bahar Tașkesen
  • Soroosh Shafieezadeh-Abadeh
  • Daniel Kuhn
  • Karthik Natarajan
    • Categories Dynamic Programming, Linear Programming, Stochastic Programming

    We study the computational complexity of the optimal transport problem that evaluates the Wasserstein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in the maximum of the number of atoms of the two distributions. However, if the components of either random vector … Read more

    Tree Bounds for Sums of Bernoulli Random Variables: A Linear Optimization Approach

  • Karthik Natarajan
  • Divya Padmanabhan
    • Categories Combinatorial Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , ,

    We study the problem of computing the tightest upper and lower bounds on the probability that the sum of n dependent Bernoulli random variables exceeds an integer k. Under knowledge of all pairs of bivariate distributions denoted by a complete graph, the bounds are NP-hard to compute. When the bivariate distributions are specified on a … Read more

    Exploiting Partial Correlations in Distributionally Robust Optimization

  • Karthyek Murthy
  • Karthik Natarajan
  • Divya Padmanabhan
    • Categories Polyhedra, Robust Optimization, Semi-definite Programming Tags , , ,

    In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, … Read more

    On the heavy-tail behavior of the distributionally robust newsvendor

  • Bikramjit Das
  • Karthik Natarajan
  • Anulekha Dhara
    • Categories Robust Optimization

    Since the seminal work of Scarf (1958) [A min-max solution of an inventory problem, Studies in the Mathematical Theory of Inventory and Production, pages 201-209] on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. The optimal order quantity is … Read more

    Distributionally Robust Linear and Discrete Optimization with Marginals

  • Louis Chen
  • Karthik Natarajan
  • David Simchi-Levi
  • Will Ma
  • Zhenzhen Yan
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Polyhedra Tags , ,

    In this paper, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to … Read more

    Distributionally Robust Markovian Traffic Equilibrium

  • Selin Damla Ahipasaoglu
  • Karthik Natarajan
  • Ugur Arikan
    • Categories Robust Optimization, Transportation Tags , ,

    Stochastic user equilibrium models are fundamental to the analysis of transportation systems. Such models are typically developed under the assumption of route based choice models for the users. A class of link based models under a Markovian assumption on the route choice behavior of the users has been proposed to deal with the drawbacks of … Read more

    Worst-Case Expected Shortfall with Univariate and Bivariate Marginals

  • Bikramjit Das
  • Karthik Natarajan
  • Anulekha Dhara
    • Categories Finance and Economics Tags , , ,

    Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert information is available in terms of bivariate … Read more

    Distributionally Robust Project Crashing with Partial or No Correlation Information

  • Selin Damla Ahipasaoglu
  • Karthik Natarajan
  • Dongjian Shi
    • Categories Robust Optimization, Semi-definite Programming

    Crashing is a method for optimally shortening the project makespan by reducing the time of one or more activities in a project network by allocating resources to it. Activity durations are however uncertain and techniques in stochastic optimization, robust optimization and distributionally robust optimization have been developed to tackle this problem. In this paper, we … Read more