Optimality Conditions for Constrained Minimax Optimization

  • Yu-Hong Dai
  • Liwei Zhang
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point problems, numerical partial differential equations and optimality conditions of equality constrained optimization. For the unconstrained continuous nonconvex-nonconcave situation, Jin, Netrapalli and Jordan (2019) carefully considered … Read more

    An algorithm for assortment optimization under parametric discrete choice models

  • Andrea Lodi
  • Tien Mai
    • Categories 0-1 Programming, Applications - OR and Management Sciences Tags , , ,

    This work concerns the assortment optimization problem that refers to selecting a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a parametric choice model. The key challenge lies in the computational difficulty of finding the best subset solution, which often requires exhaustive search. The … Read more

    Regret in the Newsvendor Model with Demand and Yield Randomness

  • Zhi Chen
  • Weijun Xie
    • Categories Robust Optimization Tags , , , , ,

    We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally … Read more

    Mixed-Integer Nonlinear Optimization for District Heating Network Expansion

  • Marius Roland
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , ,

    We present a mixed-integer nonlinear optimization model for computing the optimal expansion of an existing tree-shaped district heating network given a number of potential new consumers. To this end, we state a stationary and nonlinear model of all hydraulic and thermal effects in the pipeline network as well as nonlinear models for consumers and the … Read more

    DMulti-MADS: Mesh adaptive direct multisearch for blackbox multiobjective optimization

  • Jean Bigeon
  • Sébastien Le Digabel
  • Ludovic Salomon
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to constrained multiobjective derivative-free optimization. This method … Read more

    A Framework for Generalized Benders’ Decomposition and Its Application to Multilevel Optimization

  • Suresh Bolusani
  • Ted K. Ralphs
    • Categories (Mixed) Integer Linear Programming, Game Theory, Stochastic Programming Tags , , ,

    We describe an algorithmic framework generalizing the well-known framework originally introduced by Benders. We apply this framework to several classes of optimization problems that fall under the broad umbrella of multilevel/multistage mixed integer linear optimization problems. The development of the abstract framework and its application to this broad class of problems provides new insights and … Read more

    A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

  • Suresh Bolusani
  • Stefano Coniglio
  • Ted K. Ralphs
  • Sahar Tahernejad
    • Categories (Mixed) Integer Linear Programming, Game Theory, Stochastic Programming Tags , , , , ,

    We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, … Read more

    On Linear Optimization over Wasserstein Balls

  • Daniel Kuhn
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more

    A Framework for Adaptive Open-pit Mining Planning under Geological Uncertainty

  • Margaret Armstrong
  • Tito Homem-de-Mello
  • Guido Lagos
  • Tomas Lagos
  • Denis Saure
    • Categories Dynamic Programming, Scheduling, Stochastic Programming Tags , , , ,

    Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity (the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard), practical instances of the problem usually involve a large to very large number of decision variables, typically of the order … Read more

    2×2-convexifications for convex quadratic optimization with indicator variables

  • Shaoning Han
  • Andrés Gómez
  • Alper Atamturk
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , , ,

    In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the bivariate case as a building block, we derive … Read more