Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations

  • M.-C. Plateau
  • Yasmin Rios-Solis
    • Categories Applications - OR and Management Sciences, Quadratic Programming, Scheduling Tags , ,

    In this work, we take advantage of the powerful quadratic programming theory to obtain optimal solutions of scheduling problems. We apply a methodology that starts, in contrast to more classical approaches, by formulating three unrelated parallel machine scheduling problems as 0–1 quadratic programs under linear constraints. By construction, these quadratic programs are non-convex. Therefore, before … Read more

    A Sample Approximation Approach for Optimization with Probabilistic Constraints

  • Shabbir Ahmed
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , , ,

    We study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample. We show that such a sample approximation problem with risk level larger than the required risk level will yield a lower bound to the true … Read more

    On the solution of fuzzy bilevel programming problems

  • Stephan Dempe
  • Tatiana Starostina
    • Categories Constrained Nonlinear Optimization, Game Theory

    In this paper we formulate the fuzzy bilevel programming problem and describe one possible approach for formulating a crisp optimization problem being attached to it. Due to the nature of fuzzy bilevel programming this is a crisp bilevel programming problem. We compare our approach with one using multicriterial optimization and show, that both approaches are … Read more

    A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization

  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Semi-definite Programming Tags , ,

    A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions … Read more

    A Filter Active-Set Trust-Region Method

  • Michael P. Friedlander
  • Nicholas I. M. Gould
  • Sven Leyffer
  • Todd S. Munson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    We develop a new active-set method for nonlinear programming problems that solves a regularized linear program to predict the active set and then fixes the active constraints to solve an equality-constrained quadratic program for fast convergence. Global convergence is promoted through the use of a filter. We show that the regularization parameter fulfills the same … Read more

    Optimization by the Fixed-Point Method, Version 2.17

  • Jalaluddin Abdullah
    • Categories Constrained Nonlinear Optimization, Linear Programming Tags , , ,

    Abstract: After developing necessary background theory, the original primal and dual are specified, and the invariant primal and dual LP’s are defined. Pairs of linear mappings are defined which establish an effectively one-to-one correspondences between solutions to the original and invariant problems. The invariant problems are recast as a fixed-point problem and precise solution conditions … Read more

    H2-optimal model reduction of MIMO systems

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
  • Paul Van Dooren
    • Categories Applications - Science and Engineering Tags , , ,

    We consider the problem of approximating a $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hat{H}(s)$ of much smaller degree. We derive the gradients of the $H_2$-norm of the approximation error and show how stationary points can be described via tangential interpolation. CitationTechnical report UCL-INMA-2007.034, Department of … Read more

    A New Class of Self-Concordant Barriers from Separable Spectral Functions

  • Javier F. Peña
  • Hristo Sendov
    • Categories Convex Optimization Tags , , ,

    Given a separable strongly self-concordant function f:Rn -> R, we show the associated spectral function F(X)= (foL)(X) is also strongly self-concordant function. In addition, there is a universal constant O such that, if f(x) is separable self-concordant barrier then O^2F(X) is a self-concordant barrier. We estimate that for the universal constant we have O

    The extremal volume ellipsoids of convex bodies, their symmetry properties, and their determination in some special cases

  • Osman Guler
  • Filiz Gurtuna
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Semi-infinite Programming Tags , , , , , , , , , , ,

    A convex body K has associated with it a unique circumscribed ellipsoid CE(K) with minimum volume, and a unique inscribed ellipsoid IE(K) with maximum volume. We first give a unified, modern exposition of the basic theory of these extremal ellipsoids using the semi-infinite programming approach pioneered by Fritz John in his seminal 1948 paper. We … Read more

    On hyperbolicity cones associated with elementary symmetric polynomials

  • Yuriy Zinchenko
    • Categories Linear, Cone and Semidefinite Programming

    Elementary symmetric polynomials can be thought of as derivative polynomials of $E_n(x)=\prod_{i=1,\ldots,n} x_i$. Their associated hyperbolicity cones give a natural sequence of relaxations for $\Re^n_+$. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence of this … Read more