A General Heuristic Method for Joint Chance-Constrained Stochastic Programs with Discretely Distributed Parameters

  • Eric B. Beier
  • Matthew W. Tanner
    • Categories Basic Sciences Applications, Meta Heuristics, Stochastic Programming Tags , , ,

    We present a general metaheuristic for joint chance-constrained stochastic programs with discretely distributed parameters. We give a reformulation of the problem that allows us to define a finite solution space. We then formulate a novel neighborhood for the problem and give methods for efficiently searching this neighborhood for solutions that are likely to be improving. … Read more

    Exact duality for optimization over symmetric cones

  • Imre Pólik
  • Tamás Terlaky
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We present a strong duality theory for optimization problems over symmetric cones without assuming any constraint qualification. We show important complexity implications of the result to semidefinite and second order conic optimization. The result is an application of Borwein and Wolkowicz’s facial reduction procedure to express the minimal cone. We use Pataki’s simplified analysis and … Read more

    Lifting Inequalities: A framework for generating strong cuts in nonlinear programs

  • Jean-Philippe P. Richard
  • Mohit Tawarmalani
    • Categories Global Optimization, Integer Programming, Nonlinear Optimization Tags , , , , ,

    In this paper, we propose lifting techniques for generating strong cuts for nonlinear programs that are globally-valid. The theory is geometric and provides intuition into lifting-based cut generation procedures. As a special case, we find short proofs of earlier results on lifting techniques for mixed-integer programs. Using convex extensions, we obtain conditions that allow sequence-independent … Read more

    On Test Sets for Nonlinear Integer Maximization

  • Shmuel Onn
  • Robert Weismantel
  • Jon Lee
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , , ,

    A finite test set for an integer maximization problem enables us to verify whether a feasible point attains the global maximum. We establish in this paper several general results that apply to integer maximization problems with nonlinear objective functions. CitationOperations Research Letters 36 (2008) 439–443ArticleDownload View PDF

    Single-layer Cuts for Multi-layer Network Design Problems

  • Georg Baier
  • Arie M.C.A. Koster
  • Sebastian Orlowski
  • Thomas Engel
  • Christian Raack
    • Categories Branch and Cut Algorithms, Cutting Plane Approaches, Telecommunications Tags , , ,

    We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints … Read more

    Generating All Efficient Extreme Points in Multiple Objective Linear Programming Problem and Its Application

  • Thi Bach Kim Nguyen
  • Tuan Thien Nguyen
    • Categories Global Optimization Theory, Multi-Criteria Optimization Tags , , ,

    In this paper, simple linear programming procedure is proposed for generating all efficient extreme points and all efficient extreme rays of a multiple objective linear programming problem (V P). As an application we solve the linear multiplicative programming associated with the problem (VP). CitationsubmittedArticleDownload View PDF

    An Inexact Newton Method for Nonconvex Equality Constrained Optimization

  • Richard H. Byrd
  • Frank E. Curtis
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the … Read more

    Exploiting separability in large-scale linear support vector machine training

  • Jacek Gondzio
  • Kristian Woodsend
    • Categories Data-Mining, Quadratic Programming Tags , , ,

    Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm … Read more

    Single Item Lot-Sizing with Nondecreasing Capacities

  • Yves Pochet
  • Laurence A. Wolsey
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Production and Logistics Tags , , ,

    We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially … Read more

    A secant method for nonsmooth optimization

  • Adil Bagirov
  • Asef Nazari
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , , ,

    The notion of a secant for locally Lipschitz continuous functions is introduced and a new algorithm to locally minimize nonsmooth, nonconvex functions based on secants is developed. We demonestrate that the secants can be used to design an algorithm to find descent directions of locally Lipschitz continuous functions. This algorithm is applied to design a … Read more