A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence

  • Sungwoo Park
    • Categories Semi-definite Programming Tags , , , ,

    Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved. Park and O’Leary proposed a constraint-reduced predictor-corrector algorithm for semidefinite programming with polynomial global convergence, but they did not show its superlinear convergence. We first develop a constraint-reduced algorithm for semidefinite programming having both polynomial global … Read more

    STABILITY OF A REGULARIZED NEWTON METHOD WITH TWO POTENTIALS

  • Boushra Abbas
    • Categories Nonlinear Optimization

    In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt regularization term acts in an open loop way. As a byproduct of our study, we can take the regularization coefficient of bounded variation. These … Read more

    A Binarisation Heuristic for Non-Convex Quadratic Programming with Box Constraints

  • Laura Galli
  • Adam N. Letchford
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming

    Non-convex quadratic programming with box constraints is a fundamental problem in the global optimization literature, being one of the simplest NP-hard nonlinear programs. We present a new heuristic for this problem, which enables one to obtain solutions of excellent quality in reasonable computing times. The heuristic consists of four phases: binarisation, convexification, branch-and-bound, and local … Read more

    Distributionally Robust Optimization with Matrix Moment Constraints: Lagrange Duality and Cutting Plane Methods

  • Yongchao Liu
  • Hailin Sun
  • Huifu Xu
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    A key step in solving minimax distributionally robust optimization (DRO) problems is to reformulate the inner maximization w.r.t. probability measure as a semiinfinite programming problem through Lagrange dual. Slater type conditions have been widely used for zero dual gap when the ambiguity set is defined through moments. In this paper, we investigate effective ways for … Read more

    Solving maximum cut problems by simulated annealing

  • Tor G.J. Myklebust
    • Categories Meta Heuristics Tags ,

    This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compares its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of Johnson, Aragon, McGeoch, and Schevon. This implementation uses no structure peculiar to the maximum cut problem, but its low … Read more

    On measures of size for convex cones

  • Alberto Seeger
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , , , ,

    By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space $\mathbb{R}^n$. We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice. Citation To appear in Journal of Convex Analysis (2015) Article Download View On measures … Read more

    Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems

  • Tianyi Lin
  • Shiqian Ma
  • Shuzhong Zhang
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance. The convergence properties of the 2-block ADMM have been studied extensively in the literature. Specifically, it has been proven that the 2-block ADMM globally converges for any penalty parameter $\gamma>0$. In this … Read more

    A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives

  • Robert M. Freund
  • Rahul Mazumder
  • Paul Grigas
    • Categories Data-Mining, Nonsmooth Optimization, Statistics Tags , , , ,

    In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS-epsilon) and least squares boosting (LS-Boost-epsilon), can be viewed as subgradient descent to minimize the loss function defined … Read more

    An Inexact Proximal Algorithm for Pseudomonotone and Quasimonotone Variational Inequalities

  • Lennin Mallma Ramirez
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Nonsmooth Optimization Tags , , ,

    In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generates by the algorithm is convergent for the pseudomonotone case and weakly convergent for the quasimonotone ones. This approach unifies the … Read more

    Risk-Averse Two-Stage Stochastic Program with Distributional Ambiguity

  • Yongpei Guan
  • Ruiwei Jiang
    • Categories Robust Optimization, Stochastic Programming

    In this paper, we develop a risk-averse two-stage stochastic program (RTSP) which explicitly incorporates the distributional ambiguity covering both discrete and continuous distributions. Starting from a set of historical data samples, we construct a confidence set for the ambiguous probability distribution through nonparametric statistical estimation of its density function. We then formulate RTSP from the … Read more