Year: 2018

A globally and linearly convergent PGM for zero-norm regularized quadratic optimization with sphere constraint

  • Shaohua Pan
  • Shujun Shujun
  • Wu Yuqia
    • Categories Bound-constrained Optimization

    This paper is concerned with the zero-norm regularized quadratic optimization with a sphere constraint, which has an important application in sparse eigenvalue problems. For this class of nonconvex and nonsmooth optimization problems, we establish the KL property of exponent 1/2 for its extended-valued objective function and develop a globally and linearly convergent proximal gradient method … Read more

    Feature selection in SVM via polyhedral k-norm

  • Manlio Gaudioso
  • Enrico Gorgone
  • Jean-Baptiste Hiriart-Urruty
    • Categories Data-Mining, Global Optimization Tags , , , ,

    We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the $\ell_0$ pseudo–norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm $\|.\|_{[k]}$, intermediate … Read more

    A class of derivative-free CG projection methods for nonsmooth equations with an application to the LASSO problem

  • Tian Maoying
  • Min Sun
    • Categories Nonlinear Systems and Least-Squares Tags , , ,

    In this paper, based on a modified Gram-Schmidt (MGS) process, we propose a class of derivative-free conjugate gradient (CG) projection methods for nonsmooth equations with convex constraints. Two attractive features of the new class of methods are: (i) its generated direction contains a free vector, which can be set as any vector such that the … Read more

    Gradient methods exploiting spectral properties

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
  • Hongchao Zhang
    • Categories Convex Optimization, Nonlinear Optimization

    We propose a new stepsize for the gradient method. It is shown that this new stepsize will converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang’s asymptotic optimal gradient method (Computational Optimization and Applications, 2006, 33(1): 73-88) is applied for minimizing quadratic objective functions. Based on this spectral property, we develop … Read more

    Adaptive regularization algorithms with inexact evaluations for nonconvex optimization

  • Stefania Bellavia
  • Benedetta Morini
  • Philippe L. Toint
  • Gianmarco Gurioli
    • Categories Constrained Nonlinear Optimization, Data-Mining, Unconstrained Optimization Tags , , , ,

    A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is beta-H\”{o}lder continuous. It features a … Read more

    A Unified Framework for Sparse Relaxed Regularized Regression: SR3

  • Aleksandr Y. Aravkin
  • Peng Zheng
  • Travis Askham
  • Steve Brunton
  • Nathan Kutz
    • Categories Nonlinear Systems and Least-Squares, Nonsmooth Optimization, Statistics Tags , , , ,

    Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, vari- able selection, and high-dimensional analysis. We propose a broad framework for sparse relaxed regularized regression, called SR3. The key idea is to solve a relaxation of … Read more

    Geometric insights and proofs on optimal inventory control policies

  • OA Kilic
  • ND van Foreest
    • Categories Applications - OR and Management Sciences Tags , , ,

    We develop a unifying framework to prove the existence of optimal policies for a large class of inventory systems. The framework is based on the transformation of the inventory control problem into a game, each round of which corresponds to a single replenishment cycle. By using parametrized optimization methods we show that finding the equilibrium … Read more

    A Distributionally Robust Analysis of the Program Evaluation and Review Technique

  • Dick den Hertog
  • Ernst Roos
    • Categories Robust Optimization, Scheduling Tags , ,

    Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is commonly used in practice as it requires specification of only a few characteristics of the activities’ duration. Moreover, its computational burden is extremely low. Over the years, four main disadvantages of PERT have … Read more

    The policy graph decomposition of multistage stochastic optimization problems

  • Oscar Dowson
    • Categories Stochastic Programming Tags , , ,

    We propose the policy graph as a way of formulating multistage stochastic optimization problems. We also propose an extension to the stochastic dual dynamic programming algorithm to solve a class of problems formulated as a policy graph. This class includes discrete-time, infinite horizon, multistage stochastic optimization problems with continuous state and control variables. ArticleDownload View … Read more

    Deterministic upper bounds in global minimization with nonlinear equality constraints

  • Christian Füllner
  • Peter Kirst
  • Oliver Stein
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory

    We address the problem of deterministically determining upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the … Read more