Month: November 2016

Fully Polynomial Time (Sigma,Pi)-Approximation Schemes for Continuous Nonlinear Newsvendor and Continuous Stochastic Dynamic Programs

  • Nir Halman
  • Giacomo Nannicini
    • Categories Approximation Algorithms, Dynamic Programming Tags , , , , ,

    We study the continuous newsvendor problem (i.e. a newsvendor problem concerning goods of a non-discrete nature, such as fresh fruit juice) and a class of stochastic dynamic programs with several application areas, such as inventory control of a continuous good, economics, and supply chain management. The class is characterized by continuous state and action spaces, … Read more

    trlib: A vector-free implementation of the GLTR method for iterative solution of the trust region problem

  • Christian Kirches
  • Andreas Potschka
  • Felix Lenders
    • Categories Optimization Software and Modeling Systems, Quadratic Programming Tags , , ,

    We describe trlib, a library that implements a Variant of Gould’s Generalized Lanczos method (Gould et al. in SIAM J. Opt. 9(2), 504–525, 1999) for solving the trust region problem. Our implementation has several distinct features that set it apart from preexisting ones. We implement both conjugate gradient (CG) and Lanczos iterations for assembly of … Read more

    Numerical solution of optimal control problems with explicit and implicit switches

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Meyer
  • Andreas Potschka
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization

    In this article, we present a unified framework for the numerical solution of optimal control problems constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized … Read more

    Special cases of the quadratic shortest path problem

  • Hao Hu
  • Renata Sotirov
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Network Optimization Tags , ,

    The quadratic shortest path problem (QSPP) is the problem of finding a path in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP known as the adjacent QSPP. It was … Read more

    Sequential Linear Programming and Particle Swarm Optimization for the optimization of energy districts

  • Stefania Bellavia
  • Elisa Riccietti
  • Stefano Sello
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In this paper we deal with the optimization of energy resources management of industrial districts, with the aim of minimizing the customer energy expenses. In a district the number of possible energy system combinations is really large, and a manual design approach might lead to a suboptimal solution. For this reason we designed a software … Read more

    Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem

  • Alper Atamturk
  • Simge Küçükyavuz
  • Birce Tezel
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalities through a … Read more

    Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

  • Anya Castillo
  • Carl D. Laird
  • Jean-Paul Watson
  • Jianfeng Liu
    • Categories Global Optimization, Integer Programming, Nonlinear Optimization Tags , ,

    We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. … Read more

    Extending the ergodic convergence rate of the proximal ADMM

  • Max L. N. Gonçalves
  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , , ,

    Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in $(0,(1+\sqrt{5})/2)$ have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iteration-complexity result to include the case in which the stepsize is equal to $(1+\sqrt{5})/2$. … Read more

    Generalized average shadow prices and bottlenecks

  • Alejandro Crema
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences Tags , , ,

    We present a generalization of the average shadow price in 0-1-Mixed Integer Linear Programming problems and its relation with bottlenecks including the analysis relative to the coefficients matrix of resource constraints. A mathematical programming approach to find the strategy for investment in resources is presented. Citation Escuela de Computación, Facultad de Ciencias, Universidad Central de … Read more

    Cyclic Coordinate Update Algorithms for Fixed-Point Problems: Analysis and Applications

  • Yat Tin Chow
  • Wotao Yin
  • Tianyu Wu
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , ,

    Many problems reduce to the fixed-point problem of solving $x=T(x)$. To this problem, we apply the coordinate-update algorithms, which update only one or a few components of $x$ at each step. When each update is cheap, these algorithms are faster than the full fixed-point iteration (which updates all the components). In this paper, we focus … Read more