Month: February 2018

An algorithmic framework based on primitive directions and nonmonotone line searches for black box problems with integer variables

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Integer Programming, Optimization Software and Modeling Systems

    In this paper, we develop a new algorithmic framework that handles black box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level of freedom when exploring the integer lattice. We first describe … Read more

    A Progressive Batching L-BFGS Method for Machine Learning

  • Raghu Bollapragada
  • Jorge Nocedal
  • Hao-Jun Shi
  • Ping Tak Peter Tang
  • Dheevatsa Mudigere
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags , , ,

    The standard L-BFGS method relies on gradient approximations that are not dominated by noise, so that search directions are descent directions, the line search is reliable, and quasi-Newton updating yields useful quadratic models of the objective function. All of this appears to call for a full batch approach, but since small batch sizes give rise … Read more

    Extensions of Yuan’s Lemma to fourth-order tensor system with applications

  • Qingzhi Yang
  • Yuning Yang
  • Yang Zhou
    • Categories Constrained Nonlinear Optimization, Semi-definite Programming

    Yuan’s lemma is a basic proposition on homogeneous quadratic function system. In this paper, we extend Yuan’s lemma to 4th-order tensor system. We first give two gen- eralized definitions of positive semidefinite of 4th-order tensor, and based on them, two extensions of Yuan’s lemma are proposed. We illustrate the difference between our ex- tensions and … Read more

    Pointed Closed Convex Sets are the Intersection of All Rational Supporting Closed Halfspaces

  • Marcel K. de Carli Silva
  • Levent Tunçel
    • Categories Convex and Nonsmooth Optimization, Integer Programming Tags ,

    We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets. Citation arXiv:1802.03296. February 2018 Article Download View Pointed Closed Convex Sets are the Intersection of All Rational Supporting Closed Halfspaces

    A realistic energy optimization model for smart-home appliances

  • Miguel F. Anjos
  • Michael David de Souza Dutra
  • Sébastien Le Digabel
    • Categories Energy Tags , , , ,

    Smart homes have the potential to achieve optimal energy consumption with appropriate scheduling. The control of smart appliances can be based on optimization models, which should be realistic and efficient. However, increased realism also implies an increase in solution time. Many of the optimization models in the literature have limitations on the types of appliances … Read more

    Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation

  • Landrieu Loïc
  • Hugo Raguet
    • Categories Biomedical Applications, Data-Mining, Nonsmooth Optimization

    We present an extension of the cut-pursuit algorithm, introduced by Landrieu and Obozinski (2017), to the graph total-variation regularization of functions with a separable nondifferentiable part. We propose a modified algorithmic scheme as well as adapted proofs of convergence. We also present a heuristic approach for handling the cases in which the values associated to … Read more

    Stochastic subgradient method converges at the rate (k^{-1/4})$ on weakly convex function

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Nonsmooth Optimization Tags , ,

    We prove that the projected stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. Article Download View Stochastic subgradient method converges at the rate (k^{-1/4})$ on weakly convex function

    On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances

  • Gabriele Eichfelder
  • Tobias Gerlach
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range … Read more

    Optimal linearized symmetric ADMM for separable convex programming

  • Jianchao Bai
  • Chang Xiaokai
  • Liu Sanyang
    • Categories Constrained Nonlinear Optimization

    Due to its wide applications and simple implementations, the Alternating Direction Method of Multipliers (ADMM) has been extensively investigated by researchers from different areas. In this paper, we focus on a linearized symmetric ADMM (LSADMM) for solving the multi- block separable convex minimization model. This LSADMM partitions the data into two group variables and updates … Read more

    Exact Semidefinite Formulations for a Class of (Random and Non-Random) Nonconvex Quadratic Programs

  • Samuel Burer
  • Yinyu Ye
    • Categories Global Optimization Theory, Quadratic Programming, Semi-definite Programming Tags , ,

    We study a class of quadratically constrained quadratic programs (QCQPs), called {\em diagonal QCQPs\/}, which contain no off-diagonal terms $x_j x_k$ for $j \ne k$, and we provide a sufficient condition on the problem data guaranteeing that the basic Shor semidefinite relaxation is exact. Our condition complements and refines those already present in the literature … Read more