Nonlinear Optimization

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

    Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models

  • Ernesto G. Birgin
  • José Mario Martínez
  • Sandra Augusta Santos
  • Philippe L. Toint
  • John L. Gardenghi
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization Tags , , ,

    The evaluation complexity of general nonlinear, possibly nonconvex,constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an $\epsilon$-approximate first-order critical point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem’s function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, … 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

    A Derivative-Free Trust-Region Algorithm for the Optimization of Functions Smoothed via Gaussian Convolution Using Adaptive Multiple Importance Sampling

  • Irina S Dolinskaya
  • Alvaro Maggiar
  • Jeremy Staum
  • Andreas Wächter
    • Categories Nonlinear Optimization

    In this paper we consider the optimization of a functional $F$ defined as the co nvolution of a function $f$ with a Gaussian kernel. We propose this type of objective function for the optimization of the output of complex computational simulations, which often present some form of deterministic noise and need to be smoothed for … Read more

    Bound-constrained polynomial optimization using only elementary calculations

  • Etienne de Klerk
  • Jean-Bernard Lasserre
  • Monique Laurent
  • Zhao Sun
    • Categories Bound-constrained Optimization, Global Optimization Theory Tags , ,

    We provide a monotone non increasing sequence of upper bounds $f^H_k$ ($k\ge 1$) converging to the global minimum of a polynomial $f$ on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper bounds in [J.B. Lasserre, A new look at nonnegativity on closed sets and polynomial optimization, SIAM … Read more

    A Flexible Coordinate Descent Method for Big Data Applications

  • Kimon Fountoulakis
  • Rachael Tappenden
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization

    We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of … Read more

    Randomized Derivative-Free Optimization of Noisy Convex Functions

  • Ruobing Chen
  • Stefan M. Wild
    • Categories Stochastic Programming, Unconstrained Optimization Tags , , ,

    We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the least-squares error between the true directional derivative of a noisy function and its finite difference approximation. We provide a convergence rate analysis of STARS for solving convex … Read more

    On the unimodality of METRIC Approximation subject to normally distributed demands

  • Thibaut Barthelemy
    • Categories Convex and Nonsmooth Optimization, Supply Chain Management, Unconstrained Optimization

    METRIC Approximation is a popular model for supply chain management. We prove that it has a unimodal objective function when the demands of the n retailers are normally distributed. That allows us to solve it with a convergent sequence. This optimization method leads us to a closed-form equation of computational complexity O(n). Its solutions are … Read more