inexact restoration

An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization

  • Everton Silva
  • Ana Luisa Custódio
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose a filter approach, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an … Read more

    Improving the global convergence of Inexact Restoration methods for constrained optimization problems

  • Roberto Andreani
  • Alberto Ramos
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization Tags , , ,

    Inexact restoration (IR) methods are an important family of numerical methods for solving constrained optimization problems with applications to electronic structures and bilevel programming among others areas. In these methods, the minimization is divided in two phases: decreasing infeasibility (feasibility phase) and improving optimality (optimality phase). The feasibility phase does not require the generated points … Read more

    Inexact Restoration for Minimization with Inexact Evaluation both of the Objective Function and the Constraints

  • Luís Felipe Bueno
  • F. Larreal
  • José Mario Martínez
    • Categories Constrained Nonlinear Optimization Tags , ,

    In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research, to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are … Read more

    A stochastic first-order trust-region method with inexact restoration for finite-sum minimization

  • Stefania Bellavia
  • Nataša Krejić
  • Benedetta Morini
  • Simone Rebegoldi
    • Categories Nonlinear Optimization Tags , , , ,

    We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. At each iteration, the function and the gradient are approximated by sampling. The sample size in gradient approximations is smaller than the sample size in function approximations and the latter is determined using a deterministic rule inspired … Read more

    An inexact restoration-nonsmooth algorithm with variable accuracy for stochastic nonsmooth convex optimization problems in machine learning and stochastic linear complementarity problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using Inexact Restoration-based adapted sample sizes. The sample size is chosen in an adaptive manner based on Inexact Restoration. The algorithm uses line search … Read more

    Economic inexact restoration for derivative-free expensive function minimization and applications

  • Ernesto G. Birgin
  • Nataša Krejić
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , , , ,

    The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- … Read more

    Iteration and evaluation complexity for the minimization of functions whose computation is intrinsically inexact

  • Ernesto G. Birgin
  • Nataša Krejić
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , ,

    In many cases in which one wishes to minimize a complicated or expensive function, it is convenient to employ cheap approximations, at least when the current approximation to the solution is poor. Adequate strategies for deciding the accuracy desired at each stage of optimization are crucial for the global convergence and overall efficiency of the … Read more

    Inexact restoration with subsampled trust-region methods for finite-sum minimization

  • Stefania Bellavia
  • Nataša Krejić
  • Benedetta Morini
    • Categories Unconstrained Optimization Tags , , , ,

    Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by randomly sampling components of the sum have received great attention. We propose a new trust-region method which employs suitable approximations of the objective function, gradient and Hessian … Read more

    Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

  • Priscila Savulski Ferreira
  • Elizabeth Wegner Karas
  • Mael Sachine
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this work we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed in two independent phases: … Read more

    Assessing the reliability of general-purpose Inexact Restoration methods

  • Ernesto G. Birgin
  • Luís Felipe Bueno
  • José Mario Martínez
    • Categories Constrained Nonlinear Optimization Tags , ,

    Inexact Restoration methods have been proved to be effective to solve constrained optimization problems in which some structure of the feasible set induces a natural way of recovering feasibility from arbitrary infeasible points. Sometimes natural ways of dealing with minimization over tangent approximations of the feasible set are also employed. A recent paper [N. Banihashemi … Read more