Month: April 2016

A stochastic program with tractable time series and affine decision rules for the reservoir management problem

  • Erick Delage
  • Charles Gauvin
  • Michel Gendreau
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , , ,

    This paper proposes a multi-stage stochastic programming formulation for the reservoir management problem. Our problem specifically consists in minimizing the risk of floods over a fixed time horizon for a multi-dimensional hydro-electrical complex. We consider well-studied linear time series model and enhance the approach to consider heteroscedasticity. Using these stochastic processes under very general distributional … Read more

    The Traveling Salesman Problem on Grids with Forbidden Neighborhoods

  • Anja Fischer
  • Philipp Hungerländer
    • Categories Combinatorial Optimization Tags , , , ,

    We introduce the Traveling Salesman Problem with forbidden neighborhoods (TSPFN). This is an extension of the Euclidean TSP in the plane where direct connections between points that are too close are forbidden. The TSPFN is motivated by an application in laser beam melting. In the production of a workpiece in several layers using this method … Read more

    Pessimistic bilevel linear optimization

  • Stephan Dempe
  • Susanne Franke
  • Guimei Luo
    • Categories Nonsmooth Optimization Tags , , , ,

    In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global … Read more

    Multistage Robust Unit Commitment with Dynamic Uncertainty Sets and Energy Storage

  • Alvaro Lorca
  • Xu Andy Sun
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , , ,

    The deep penetration of wind and solar power is a critical component of the future power grid. However, the intermittency and stochasticity of these renewable resources bring significant challenges to the reliable and economic operation of power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the unit commitment (UC) … Read more

    On the Grassmann condition number

  • Javier F. Peña
  • Vera Roshchina
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We give new insight into the Grassmann condition of the conic feasibility problem \[ x \in L \cap K \setminus\{0\}. \] Here $K\subseteq V$ is a regular convex cone and $L\subseteq V$ is a linear subspace of the finite dimensional Euclidean vector space $V$. The Grassmann condition of this problem is the reciprocal of the … Read more

    Analysis of transformations of linear random-effects models

  • Yongge Tian
    • Categories Statistics Tags , , , , ,

    Assume that a linear random-effects model (LRM) $\by = \bX \bbe + \bve = \bX\bbe+ \bve$ with $\bbe = \bA \bal + \bga$ is transformed as $\bT\by = \bT\bX\bbe + \bT\bve = \bT\bX\bA \bal + \bT\bX\bga + \bT\bve$ by pre-multiplying a given matrix $\bT$. Estimations/predictions of the unknown parameters under the two models are not … Read more

    Approximation Properties and Tight Bounds for Constrained Mixed-Integer Optimal Control

  • Christian Kirches
  • Felix Lenders
  • Paul Manns
    • Categories Approximation Algorithms, Complementarity and Variational Inequalities, Systems governed by Differential Equations Optimization

    We extend recent work on mixed-integer nonlinear optimal control prob- lems (MIOCPs) to the case of integer control functions subject to constraints. Promi- nent examples of such systems include problems with restrictions on the number of switches permitted, or problems that minimize switch cost. We extend a theorem due to [Sager et al., Math. Prog. … Read more

    Toward computer-assisted discovery and automated proofs of cutting plane theorems

  • Matthias Köppe
  • Yuan Zhou
    • Categories Cutting Plane Approaches, Optimization Software and Modeling Systems

    Using a metaprogramming technique and semialgebraic computations, we provide computer-based proofs for old and new cutting-plane theorems in Gomory–Johnson’s model of cut generating functions. Citation to be presented at ISCO 2016 Article Download View Toward computer-assisted discovery and automated proofs of cutting plane theorems

    Algorithms for stochastic optimization with expectation constraints

  • Guanghui Lan
  • Zhiqiang Zhou
    • Categories Bound-constrained Optimization, Convex and Nonsmooth Optimization, Stochastic Programming Tags , , , ,

    This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with an expectation constraint on either decision variables or problem parameters. We first present a new stochastic approximation (SA) type algorithm, namely the cooperative SA (CSA), to handle problems with the expectation constraint on devision variables. We show that … Read more

    A Polyhedral Approach to Online Bipartite Matching

  • Shabbir Ahmed
  • Alejandro Toriello
  • Alfredo Torrico
    • Categories Dynamic Programming, Polyhedra Tags , ,

    We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of a uniform distribution, and must immediately be matched or discarded. We consider various … Read more