Rohit Kannan

Optimality-Based Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs

  • Evren Turan
  • Johannes Jäschke
  • Rohit Kannan
    • Categories Global Optimization, Semi-infinite Programming Tags , , , , ,

    We use sensitivity analysis to design optimality-based discretization (cutting-plane) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal discretization of SIPs as a max-min problem and propose variants that are more computationally tractable. We then use parametric sensitivity theory to design an efficient method for solving these max-min … Read more

    Strong Partitioning and a Machine Learning Approximation for Accelerating the Global Optimization of Nonconvex QCQPs

  • Rohit Kannan
  • Harsha Nagarajan
  • Deepjyoti Deka
    • Categories Global Optimization Tags , , , , , ,

    We learn optimal instance-specific heuristics for the global minimization of nonconvex quadratically-constrained quadratic programs (QCQPs). Specifically, we consider partitioning-based convex mixed-integer programming relaxations for nonconvex QCQPs and propose the novel problem of strong partitioning to optimally partition variable domains without sacrificing global optimality. Since solving this max-min strong partitioning problem exactly can be very challenging, … Read more

    Heteroscedasticity-aware residuals-based contextual stochastic optimization

  • Rohit Kannan
  • Güzin Bayraksan
  • James R. Luedtke
    • Categories Robust Optimization, Stochastic Programming Tags , , , , , ,

    We explore generalizations of some integrated learning and optimization frameworks for data-driven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation process, and the prediction setup under which these generalizations possess asymptotic and finite sample guarantees for a class of stochastic programs, including two-stage stochastic mixed-integer programs … Read more

    Residuals-based distributionally robust optimization with covariate information

  • Rohit Kannan
  • Güzin Bayraksan
  • James R. Luedtke
    • Categories Robust Optimization, Stochastic Programming Tags , , , , , , ,

    We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained … Read more

    Data-driven sample average approximation with covariate information

  • Rohit Kannan
  • Güzin Bayraksan
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , , , ,

    We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning … Read more

    Stochastic DC Optimal Power Flow With Reserve Saturation

  • Rohit Kannan
  • James R. Luedtke
  • Line Roald
    • Categories Applications - Science and Engineering, Stochastic Programming Tags , , , ,

    We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator’s target level hits … Read more

    A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

  • Rohit Kannan
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , ,

    We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. To this end, we construct a reformulated problem whose objective is to minimize … Read more