Unconstrained Optimization

A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization: complete results

  • Giovanni Fasano
  • Stefano Lucidi
    • Categories Unconstrained Optimization Tags , , , ,

    We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative … Read more

    Descent heuristics for unconstrained minimization

  • Florian Jarre
  • Ania Lopez
    • Categories Global Optimization, Unconstrained Optimization Tags , ,

    Semidefinite relaxations often provide excellent starting points for nonconvex problems with multiple local minimizers. This work aims to find a local minimizer within a certain neighborhood of the starting point and with a small objective value. Several approaches are motivated and compared with each other. Citation Report, Mathematisches Institut, Universitaet Duesseldorf, August 2008. Article Download … Read more

    Optimal steepest descent algorithms for unconstrained convex problems: fine tuning Nesterov’s method

  • Clóvis Caesar Gonzaga
  • Elizabeth Wegner Karas
    • Categories Convex Optimization, Unconstrained Optimization Tags ,

    We modify the first order algorithm for convex programming proposed by Nesterov. The resulting algorithm keeps the optimal complexity obtained by Nesterov with no need of a known Lipschitz constant for the gradient, and performs better in practically all examples in a set of test problems. Citation Technical Report, Federal University of Santa Catarina, 2008. … Read more

    A stochastic algorithm for function minimization

  • Su Dongcai
  • Dong Junwei
  • Zheng Zuduo
    • Categories Constrained Nonlinear Optimization, Stochastic Approaches, Unconstrained Optimization Tags , ,

    Focusing on what an optimization problem may comply with, the so-called convergence conditions have been proposed and sequentially a stochastic optimization algorithm named as DSZ algorithm is presented in order to deal with both unconstrained and constrained optimizations. Its principle is discussed in the theoretical model of DSZ algorithm, from which we present a practical … Read more

    ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

  • Rommel Regis
  • Christine Shoemaker
  • Stefan M. Wild
    • Categories Optimization of Simulated Systems, Unconstrained Optimization Tags , , ,

    We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by … Read more

    Extended Barzilai-Borwein method for unconstrained minimization problems

  • Yasushi Narushima
  • Hiroshi Yabe
  • Takahiko Wakamatsu
    • Categories Unconstrained Optimization Tags , ,

    In 1988, Barzilai and Borwein presented a new choice of step size for the gradient method for solving unconstrained minimization problems. Their method aimed to accelerate the convergence of the steepest descent method. The Barzilai-Borwein method requires few storage locations and inexpensive computations. Therefore, several authors have paid attention to the Barzilai-Borwein method and have … Read more

    Accelerated line-search and trust-region methods

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
    • Categories Applications - Science and Engineering, Unconstrained Optimization Tags , , ,

    In numerical optimization, line-search and trust-region methods are two important classes of descent schemes, with well-understood global convergence properties. Here we consider “accelerated” versions of these methods, where the conventional iterate is allowed to be replaced by any point that produces at least as much decrease in the cost function as a fixed fraction of … Read more

    A subspace minimization method for the trust-region step

  • Jennifer B. Erway
  • Philip E. Gill
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    We consider methods for large-scale unconstrained minimization based on finding an approximate minimizer of a quadratic function subject to a two-norm trust-region constraint. The Steihaug-Toint method uses the conjugate-gradient (CG) algorithm to minimize the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the constraint boundary. … Read more

    Benchmarking Derivative-Free Optimization Algorithms

  • Jorge Moré
  • Stefan M. Wild
    • Categories Optimization Software Benchmark, Unconstrained Optimization Tags , , , ,

    We propose data profiles as a tool for analyzing the performance of derivative-free optimization solvers when there are constraints on the computational budget. We use performance and data profiles, together with a convergence test that measures the decrease in function value, to analyze the performance of three solvers on sets of smooth, noisy, and piecewise-smooth … Read more

    Primal interior point method for minimization of generalized minimax functions

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

    In this report, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning … Read more