Nonlinear Optimization

Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite Programming

  • Deren Han
  • Defeng Sun
  • Liwei Zhang
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , ,

    In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain error bound condition, we establish the global linear rate of convergence for a more general semi-proximal ADMM with the dual steplength … Read more

    The Uncapacitated Single Allocation p-Hub Median Problem with Stepwise Cost Function

  • Christoph Buchheim
  • Borzou Rostami
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Quadratic Programming Tags , ,

    In this paper, we address a new version of the Uncapacitated Single Allocation p-Hub Median Problem (USApHMP) in which transportation costs on each edge are given by piecewise constant cost functions. In the classical USApHMP, transportation costs are modelled as linear functions of the transport volume, where a fixed discount factor on hub-hub connections is … Read more

    A DERIVATIVE-FREE APPROACH TO CONSTRAINED MULTIOBJECTIVE NONSMOOTH OPTIMIZATION

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this … Read more

    The Sparse PCA Problem: Optimality Conditions and Algorithms

  • Amir Beck
  • Yakov Vaisbourd
    • Categories Nonlinear Optimization

    Sparse principal component analysis (PCA) addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components, and is applicable in a wide variety of fields including genetics and … Read more

    Bounded perturbation resilience of projected scaled gradient methods

  • Yair Censor
  • Ming Jiang
  • Wenma Jin
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , ,

    We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, … Read more

    On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming

  • Xin Liu
  • Ya-Feng Liu
  • Shiqian Ma
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags ,

    In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian (AL) subproblem in the proposed IAL framework is … Read more

    Cutting Box Strategy: an algorithmic framework for improving metaheuristics for continuous global optimization

  • Marcia Fampa
  • Wendel Melo
  • Fernanda M. P. Raupp
    • Categories Constrained Nonlinear Optimization, Stochastic Approaches Tags , , ,

    In this work, we present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. … Read more

    Discrete flow pooling problems in coal supply chains

  • Natashia Boland
  • Thomas Kalinowski
  • Fabian Rigterink
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Global Optimization Applications

    The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate … Read more

    Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

  • Priscila Savulski Ferreira
  • Elizabeth Wegner Karas
  • Mael Sachine
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this work we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed in two independent phases: … Read more

    A special case of the generalized pooling problem arising in the mining industry

  • Natashia Boland
  • Thomas Kalinowski
  • Fabian Rigterink
  • Martin Savelsbergh
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications

    Iron ore and coal are substantial contributors to Australia’s export economy. Both are blended products that are made-to-order according to customers’ desired product qualities. Mining companies have a great interest in meeting these target qualities since deviations generally result in contractually agreed penalties. This paper studies a variation of the generalized pooling problem (GPP) arising … Read more