A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization: complete results

  • Giovanni Fasano
  • Stefano Lucidi
    • Categories Unconstrained Optimization Tags , , , ,

    We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative … Read more

    Gradient based method for cone programming with application to large-scale compressed sensing

  • Zhaosong Lu
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Statistics Tags

    In this paper, we study a gradient based method for general cone programming (CP) problems. In particular, we first consider four natural primal-dual convex smooth minimization reformulations for them, and then discuss a variant of Nesterov’s smooth (VNS) method recently proposed by Tseng [30] for solving these reformulations. The associated worst-case major arithmetic operations costs … Read more

    Dantzig-Wolfe and block coordinate-descent decomposition in large-scale integrated refinery-planning

  • Adebayo Alabi
  • Jordi Castro
    • Categories Applications - Science and Engineering, Chemical Engineering Tags , , ,

    The integrated refinery-planning (IRP), an instrumental problem in the petroleum industry, is made of several subsystems, each of them involving a large number of decisions. Despite the complexity of the overall planning problem, this work presents a mathematical model of the refinery operations char acterized by complete horizontal integration of subsystems from crude oil purchase … Read more

    Quadratic regularizations in an interior-point method for primal block-angular problems

  • Jordi Castro
  • Jordi Cuesta
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming

    One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectral radius—in [0,1)—of a certain matrix in the definition of the preconditioner. Spectral radius close … Read more

    Necessary Conditions for the Impulsive Optimal Control of Multibody Mechanical Systems

  • Kerim Yunt
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , , ,

    In this work, necessary conditions for the impulsive optimal control of multibody mechanical systems are stated. The conditions are obtained by the application subdifferential calculus techniques to extended-valued lower semi-continuous generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered … Read more

    Dynamic Subgradient Methods

  • Grégory Emiel
  • Claudia Sagastizábal
    • Categories Cutting Plane Approaches, Nonsmooth Optimization

    Lagrangian relaxation is commonly used to generate bounds for mixed-integer linear programming problems. However, when the number of dualized constraints is very large (exponential in the dimension of the primal problem), explicit dualization is no longer possible. In order to reduce the dual dimension, different heuristics were proposed. They involve a separation procedure to dynamically … Read more

    Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Spaces

  • Yair Censor
  • Aviv Gibali
    • Categories Complementarity and Variational Inequalities Tags , ,

    The variational inequality problem (VIP) is considered here. We present a general algorithmic scheme which employs projections onto hyperplanes that separate balls from the feasible set of the VIP instead of projections onto the feasible set itself. Our algorithmic scheme includes the classical projection method and Fukushima’s subgradient projection method as special cases. CitationTechnical report: … Read more

    The Facility Location Problem with Bernoulli Demands

  • Maria Albareda-Sambola
  • Francisco Saldanha-da-Gama
  • Elena Fernandez
    • Categories Stochastic Programming Tags ,

    In this paper we address a discrete capacitated facility location problem in which customers have Bernoulli demands. The problem is formulated as a two-stage stochastic program. The goal is to define an a priori solution for the location of the facilities and for the allocation of customers to the operating facilities that minimize the expected … Read more

    An SDP-based divide-and-conquer algorithm for large scale noisy anchor-free graph realization

  • Ngai-Hang Z. Leung
  • Kim-Chuan Toh
    • Categories Basic Sciences Applications, Global Optimization Applications, Semi-definite Programming Tags , , ,

    We propose the DISCO algorithm for graph realization in $\real^d$, given sparse and noisy short-range inter-vertex distances as inputs. Our divide-and-conquer algorithm works as follows. When a group has a sufficiently small number of vertices, the basis step is to form a graph realization by solving a semidefinite program. The recursive step is to break … Read more