Month: September 2015

Solving conic optimization problems via self-dual embedding and facial reduction: a unified approach

  • Erling D. Andersen
  • Henrik A. Friberg
  • Frank Permenter
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    We establish connections between the facial reduction algorithm of Borwein and Wolkowicz and the self-dual homogeneous model of Goldman and Tucker when applied to conic optimization problems. Specifically, we show the self-dual homogeneous model returns facial reduction certificates when it fails to return a primal-dual optimal solution or a certificate of infeasibility. Using this observation, … Read more

    Simple Approximations of Semialgebraic Sets and their Applications to Control

  • Fabrizio Dabbene
  • Didier Henrion
  • Constantino Lagoa
    • Categories Control Applications, Semi-definite Programming, Statistics Tags , , ,

    Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance the solution set of linear matrix inequalities or the Schur/Hurwitz stability domains. These sets often have very complicated shapes … Read more

    A Quantitative Comparison of Risk Measures

  • Alois Pichler
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags ,

    The choice of a risk measure reflects a subjective preference of the decision maker in many managerial, or real world economic problem formulations. To evaluate the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We … Read more

    Nonstationary Direct Policy Search for Risk-Averse Stochastic Optimization

  • Belgacem Bouzaiene-Ayari
  • Somayeh Moazeni
  • Boris Defourny
  • Warren B. Powell
    • Categories Dynamic Programming, Parallel Algorithms, Stochastic Programming Tags , ,

    This paper presents an approach to non-stationary policy search for finite-horizon, discrete-time Markovian decision problems with large state spaces, constrained action sets, and a risk-sensitive optimality criterion. The methodology relies on modeling time variant policy parameters by a non-parametric response surface model for an indirect parametrized policy motivated by the Bellman equation. Through the interpolating … Read more

    The Ramping Polytope and Cut Generation for the Unit Commitment Problem

  • Bernard Knueven
  • James Ostrowski
  • Jianhui Wang
    • Categories Applications - OR and Management Sciences Tags , ,

    We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramping constraints, time-dependent start-up costs, and start-up/shut-down ramping. To develop this perfect formulation we extend the result of Balas on unions of polyhedra … Read more

    Linear conic formulations for two-party correlations and values of nonlocal games

  • Jamie Sikora
  • Antonios Varvitsiotis
    • Categories Applications - Science and Engineering, Graphs and Matroids, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify … Read more

    Solving MIPs via Scaling-based Augmentation

  • Pierre Le Bodic
  • Marc E. Pfetsch
  • Sebastian Pokutta
  • Jeffrey W. Pavelka
    • Categories (Mixed) Integer Linear Programming Tags , ,

    Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e., number of iterations needed, can theoretically be improved by scaling methods. We extend these results by an … Read more

    Construction of IMEX DIMSIMs of high order and stage order

  • Z. Jackiewicz
  • Hans D Mittelmann
    • Categories Applications - Science and Engineering Tags , , , , ,

    For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stff or mildly stff, and the other part is stff. Such systems can be effciently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration … Read more

    Strong Duality: Without Simplex and without theorems of alternatives

  • Somdeb Lahiri
    • Categories Linear Programming Tags , ,

    The simplex method has its own problems related to degenerate basic feasible solutions. While such solutions are infrequent, from a theoretical standpoint a proof of the strong duality theorem that uses the simplex method is not complete until it has taken a few extra steps. Further, for economists the duality theorem is extremely important whereas … Read more

    A basis-free null space method for solving generalized saddle point problems

  • Maria A. Diniz-Ehrhardt
  • Lucas G. Pedroso
  • Douglas Mendes
    • Categories Constrained Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , , , , , , ,

    Using an augmented Lagrangian matrix approach, we analytically solve in this paper a broad class of linear systems that includes symmetric and nonsymmetric problems in saddle point form. To this end, some mild assumptions are made and a preconditioning is specially designed to improve the sensitivity of the systems before the calculation of their solutions. … Read more