Stochastically Constrained Simulation Optimization On Integer-Ordered Spaces: The cgR-SPLINE Algorithm

  • Kalyani Nagaraj
  • Raghu Pasupathy
    • Categories Global Optimization, Integer Programming, Stochastic Programming Tags , ,

    We consider the problem of identifying the solution(s) to an optimization problem whose domain is a subset of the integer lattice, and whose objective and constraint functions can only be observed using a stochastic simulation. Such problems seem particularly prevalent (see www.simopt.org) within service systems having capacity or service-level constraints. We present cgR-SPLINE — a … Read more

    The Lyapunov rank of an improper cone

  • Michael Orlitzky
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming Tags , , , ,

    Let K be a closed convex cone with dual K^* in a finite-dimensional real inner-product space V. The complementarity set of K is C(K) = { (x, s) in K × K^* | = 0 }. We say that a linear transformation L : V -> V is Lyapunov-like on K if = 0 for all (x, … Read more

    A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

  • H. C. F. Apolinário
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
  • Kely Diana Villacorta
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Unconstrained Optimization

    In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal parameters are bounded we prove the convergence of the sequence generated by the algorithm and when the objective functions are continuous, we prove the … Read more

    A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

  • H. C. F. Apolinário
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
  • Kely Diana Villacorta
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Unconstrained Optimization

    In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal parameters are bounded we prove the convergence of the sequence generated by the algorithm and when the objective functions are continuous, we prove the … Read more

    Robust Markov Decision Processes for Medical Treatment Decisions

  • Brian T. Denton
  • Lauren Steimle
  • Yuanhui Zhang
    • Categories Applications - Science and Engineering, Biomedical Applications, Robust Optimization

    Medical treatment decisions involve complex tradeoffs between the risks and benefits of various treatment options. The diversity of treatment options that patients can choose over time and uncertainties in future health outcomes, result in a difficult sequential decision making problem. Markov decision processes (MDPs) are commonly used to study medical treatment decisions; however, optimal policies … Read more

    A new lift-and-project operator

  • Merve Bodur
  • Sanjeeb Dash
  • Oktay Gunluk
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , ,

    In this paper, we analyze the strength of split cuts in a lift-and-project framework. We first observe that the Lovasz-Schrijver and Sherali-Adams lift-and-project operator hierarchies can be viewed as applying specific 0-1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts. More precisely, we define a … Read more

    Distributionally Robust Logistic Regression

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high … Read more

    Manifold Sampling for L1 Nonconvex Optimization

  • Jeffrey Larson
  • Matt Menickelly
  • Stefan M. Wild
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function $h\circ F$ when $h$ has known structure. In particular, by classifying points in the domain of the nonsmooth function $h$ into manifolds, we adapt search directions within a trust-region framework based on knowledge of manifolds intersecting the current … Read more

    Adaptive Elective Surgery Planning Under Duration and Length-Of-Stay Uncertainty: A Robust Optimization Approach

  • Bjorn Berg
  • Saba Neyshabouri
    • Categories Cutting Plane Approaches, Robust Optimization, Scheduling Tags , , ,

    Scheduling elective surgeries is a complicated task due to the coupled effect of multiple sources of uncertainty and the impact of the proposed schedule on the downstream units. In this paper, we propose an adaptive robust optimization model to address the existing uncertainty in surgery duration and length-of-stay in the surgical intensive care unit. The … Read more

    On Cournot-Nash-Walras equilibria and their computation

  • Michal Cervinka
  • Michael C. Ferris
  • Jiri V. Outrata
    • Categories Nonsmooth Optimization Tags , , , , ,

    This paper considers a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/ rms who share a certain amount of a so-called rare resource needed for their production, and the Walras equilibrium determines the price of that rare resource. We prove the existence of … Read more