trust-region methods

Density-based Globally Convergent Trust-Region Methods for Self-Consistent Field Electronic Structure Calculations

  • Juliano B. Francisco
  • Leandro Martínez
  • José Mario Martínez
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix … Read more

    Regularization Using a Parameterized Trust Region Subproblem

  • Oleg Grodzevich
  • Henry Wolkowicz
    • Categories Applications - Science and Engineering, Biomedical Applications, Nonlinear Systems and Least-Squares Tags , , , ,

    We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional {\em trust-region subproblem}, \TRS, approach that makes use of the {\em L-curve} maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We … Read more

    On the Global Convergence of a Trust Region Method for Solving Nonlinear Constraints Infeasibility Problem

  • Choong Ming Chin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    A framework for proving global convergence for a class of nonlinear constraints infeasibility problem is presented without assuming that the Jacobian has full rank everywhere. The underlying method is based on the simple sufficient reduction criteria where trial points are accepted provided there is a sufficient decrease in the constraints violation function. The proposed methods … Read more

    Magnetic Resonance Tissue Density Estimation using Optimal SSFP Pulse-Sequence Design

  • Christopher Anand
  • Renata Sotirov
  • Tamás Terlaky
  • Zhuo Zheng
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , ,

    In this paper, we formulate a nonlinear, nonconvex semidefinite optimization problem to select the steady-state free precession (SSFP) pulse-sequence design variables which maximize the contrast to noise ratio in tissue segmentation. The method could be applied to other pulse sequence types, arbitrary numbers of tissues, and numbers of images. To solve the problem we use … Read more

    Finding optimal algorithmic parameters using a mesh adaptive direct search

  • Charles Audet
  • Dominique Orban
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algorithmic parameters. This is done by devising a general framework for parameter tuning. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of … Read more

    A shifted Steihaug-Toint method for computing a trust-region step.

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Unconstrained Optimization Tags , , , , ,

    Trust-region methods are very convenient in connection with the Newton method for unconstrained optimization. The More-Sorensen direct method and the Steihaug-Toint iterative method are most commonly used for solving trust-region subproblems. We propose a method which combines both of these approaches. Using the small-size Lanczos matrix, we apply the More-Sorensen method to a small-size trust-region … Read more

    Sensitivity of trust-region algorithms on their parameters

  • Nicholas I. M. Gould
  • Dominique Orban
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Unconstrained Optimization Tags , ,

    In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommanded ranges of values for these parameters are … Read more

    A Trust-Region Algorithm for Global Optimization

  • Bernardetta Addis
  • Sven Leyffer
    • Categories Stochastic Approaches Tags , ,

    We consider the global minimization of a bound-constrained function with a so-called funnel structure. We develop a two-phase procedure that uses sampling, local optimization, and Gaussian smoothing to construct a smooth model of the underlying funnel. The procedure is embedded in a trust-region framework that avoids the pitfalls of a fixed sampling radius. We present … Read more

    A modified nearly exact method for solving low-rank trust region subproblem

  • Zhaosong Lu
  • Renato D.C. Monteiro
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper we present a modified nearly exact (MNE) method for solving low-rank trust region (LRTR) subproblem. The LRTR subproblem is to minimize a quadratic function, whose Hessian is a positive diagonal matrix plus explicit low-rank update, subject to a Dikin-type ellipsoidal constraint, whose scaling matrix is positive definite and has the similar structure … Read more

    Intermediate Report on the development of an optimization code for smooth, high computing load, continuous objective functions when derivatives are not available

  • Frank Vanden Berghen
    • Categories Multidisciplinary Design Optimization, Unconstrained Optimization Tags ,

    We find very often in the industry simulators of huge chemical reactors, simulators of huge turbo-compressors, simulators of the path of a satellite in low orbit around earth, … These simulators were written to allow the design engineer to correctly estimate the consequences of the adjustment of one (or many) design variables (or parameters of … Read more