Trust Region Method

Sub-sampled Trust-Region Methods with Deterministic Worst-Case Complexity Guarantees

  • Max L. N. Gonçalves
  • Geovani Nunes Grapiglia
    • Categories Unconstrained Optimization Tags , , ,

    In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function, significantly reducing the overall computational cost. We propose a novel adaptive procedure for deterministically adjusting the sample size used for gradient (or gradient and Hessian) … Read more

    SMOP: Stochastic trust region method for multi-objective problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Luka Rutešić
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The problem considered is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate functions and … Read more

    Convergence to a second-order critical point of composite nonsmooth problems by a trust region method

  • Hiroshi Yamashita
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    An algorithm for finding a first-order and second-order critical point of composite nonsmooth problems is proposed in this paper. For smooth problems, algorithms for searching such a point usually utilize the so called negative-curvature directions. In this paper, the method recently proposed for nonlinear semidefinite problems by the current author is extended for solving general … Read more

    An Adaptive Trust-Region Method Without Function Evaluations

  • Geovani Nunes Grapiglia
  • Gabriel Stella
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we propose an adaptive trust-region method for smooth unconstrained optimization. The update rule for the trust-region radius relies only on gradient evaluations. Assuming that the gradient of the objective function is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations required by the proposed method to generate approximate … Read more

    A Trust Region Method for the Optimization of Noisy Functions

  • Shigeng Sun
  • Jorge Nocedal
    • Categories Nonlinear Optimization Tags , ,

    Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about … Read more