derivative-free optimization

A derivative-free trust-funnel method for equality-constrained nonlinear optimization

  • Phillipe Sampaio
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this work, we look into new derivative-free methods to solve equality-constrained optimization problems. Of particular interest, are the trust-region techniques, which have been investigated for the unconstrained and bound-constrained cases. For solving equality-constrained optimization problems, we introduce a derivative-free adaptation of the trust-funnel method combined with a self-correcting geometry scheme and present some encouraging … Read more

    A Linesearch-based Derivative-free Approach for Nonsmooth Optimization

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

    In this paper, we propose new linesearch-based methods for nonsmooth optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence towards stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequality constrained optimization … Read more

    Convergence of trust-region methods based on probabilistic models

  • A. S. Bandeira
  • Katya Scheinberg
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , ,

    In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic optimization approaches in two principal ways. Firstly, we assume that the value of the function itself can be computed without noise, in … Read more

    Worst case complexity of direct search under convexity

  • M. Dodangeh
  • Luis Nunes Vicente
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same global rate or worst case complexity bound of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that … Read more

    A merit function approach for direct search

  • Serge Gratton
  • Luis Nunes Vicente
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , ,

    In this paper it is proposed to equip direct-search methods with a general procedure to minimize an objective function, possibly non-smooth, without using derivatives and subject to constraints on the variables. One aims at considering constraints, most likely nonlinear or non-smooth, for which the derivatives of the corresponding functions are also unavailable. The novelty of … Read more

    Reducing the Number of Function Evaluations in Mesh Adaptive Direct Search Algorithms

  • Charles Audet
  • Sébastien Le Digabel
  • Christophe Tribes
  • Andrea Ianni
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    The mesh adaptive direct search (MADS) class of algorithms is designed for nonsmooth optimization, where the objective function and constraints are typically computed by launching a time-consuming computer simulation. Each iteration of a MADS algorithm attempts to improve the current best-known solution by launching the simulation at a finite number of trial points. Common implementations … Read more

    Efficient Cardinality/Mean-Variance Portfolios

  • R. P. Brito
  • Luis Nunes Vicente
    • Categories Finance and Economics, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , ,

    A number of variants of the classical Markowitz mean-variance optimization model for portfolio selection have been investigated to render it more realistic. Recently, it has been studied the imposition of a cardinality constraint, setting an upper bound on the number of active positions taken in the portfolio, in an attempt to improve its performance and … Read more

    Smoothing and Worst Case Complexity for Direct-Search Methods in Non-Smooth Optimization

  • R. Garmanjani
  • Luis Nunes Vicente
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    For smooth objective functions it has been shown that the worst case cost of direct-search methods is of the same order as the one of steepest descent, when measured in number of iterations to achieve a certain threshold of stationarity. Motivated by the lack of such a result in the non-smooth case, we propose, analyze, … Read more

    Inexact Restoration method for Derivative-Free Optimization with smooth constraints

  • Luís Felipe Bueno
  • A. Friedlander
  • José Mario Martínez
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems Tags , , ,

    A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the Inexact Restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only … Read more

    Sobolev Seminorm of Quadratic Functions with Applications to Derivative-Free Optimization

  • Zaikun Zhang
    • Categories Unconstrained Optimization Tags , , ,

    This paper studies the $H^1$ Sobolev seminorm of quadratic functions. The research is motivated by the least-norm interpolation that is widely used in derivative-free optimization. We express the $H^1$ seminorm of a quadratic function explicitly in terms of the Hessian and the gradient when the underlying domain is a ball. The seminorm gives new insights … Read more