trust-region methods

A globally convergent trust-region algorithm for unconstrained derivative-free optimization

  • Priscila Savulski Ferreira
  • Elizabeth Wegner Karas
  • Mael Sachine
    • Categories Nonlinear Optimization, Other Topics, Unconstrained Optimization Tags , , ,

    In this work we explicit a derivative-free trust-region algorithm for unconstrained optimization based on the paper (Computational Optimization and Applications 53: 527-555, 2012) proposed by Powell. The objective function is approximated by quadratic models obtained by polynomial interpolation. The number of points of the interpolation set is fixed. In each iteration only one interpolation point … Read more

    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 Trust Region Method for the Solution of the Surrogate Dual in Integer Programming

  • Natashia Boland
  • Andrew C. Eberhard
  • Angelos Tsoukalas
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Nonsmooth Optimization Tags , ,

    We propose an algorithm for solving the surrogate dual of a mixed integer program. The algorithm uses a trust region method based on a piecewise affine model of the dual surrogate value function. A new and much more flexible way of updating bounds on the surrogate dual’s value is proposed, which numerical experiments prove to … Read more

    An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

  • Frank E. Curtis
  • Nicholas I. M. Gould
  • Daniel P. Robinson
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, … Read more

    A Two-Variable Approach to the Two-Trust-Region Subproblem

  • Samuel Burer
  • Boshi Yang
    • Categories Quadratic Programming, Semi-definite Programming Tags , ,

    The trust-region subproblem minimizes a general quadratic function over an ellipsoid and can be solved in polynomial time using a semidefinite-programming (SDP) relaxation. Intersecting the feasible set with a second ellipsoid results in the two-trust-region subproblem (TTRS). Even though TTRS can also be solved in polynomial-time, existing algorithms do not use SDP. In this paper, … Read more

    Narrowing the difficulty gap for the Celis-Dennis-Tapia problem

  • Immanuel M. Bomze
  • Michael L. Overton
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Quadratic Programming Tags , , , ,

    We study the {\em Celis-Dennis-Tapia (CDT) problem}: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that … Read more

    Polynomial solvability of variants of the trust-region subproblem

  • Daniel Bienstock
  • Alexander Michalka
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , ,

    The trust region subproblem concerns the minimization of a general quadratic over the unit ball in R^n. Extensions to this problem are of interest because of applications to, for example, combinatorial optimization. However the extension obtained by adding an arbitrary family of linear side constraints is NP-hard. In this paper we consider variants of the … Read more

    A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Kely Diana Villacorta
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , , ,

    Multiobjective optimization has a significant number of real life applications. For this reason, in this paper, we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used by \citet{conn} to establish … 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