constrained optimization

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

    Hierarchically constrained multi-fidelity blackbox optimization

  • Xavier Lebeuf
  • Sébastien Le Digabel
  • Charles Audet
  • Miguel Diago
  • Stéphane Alarie
    • Categories Constrained Nonlinear Optimization, Energy, Nonsmooth Optimization Tags , , , , ,

    This work introduces a novel multi-fidelity blackbox optimization algorithm designed to alleviate the resource-intensive task of evaluating infeasible points. This algorithm is an intermediary component bridging a direct search solver and a blackbox, resulting in reduced computation time per evaluation, all while preserving the efficiency and convergence properties of the chosen solver. This is made … Read more

    First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Points

  • Zhichao Jia
  • Benjamin Grimmer
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show a simple first-order method finds a feasible, ϵ-stationary point at a convergence rate of O(ϵ−4) without relying on compactness or Constraint Qualification (CQ). When CQ holds, this convergence is measured by … Read more

    An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization

  • Albert S. Berahas
  • Raghu Bollapragada
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the gradient in conjunction with inexact solutions to the SQP subproblems. Under reasonable … Read more

    Handling of constraints in multiobjective blackbox optimization

  • Jean Bigeon
  • Sébastien Le Digabel
  • Ludovic Salomon
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where research of a feasible … Read more

    A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization

  • Yonggang Pei
  • Shaofang Song
  • Zhu Detong
    • Categories Constrained Nonlinear Optimization Tags , , ,

    The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this paper, we extend ARC to solve nonlinear equality constrained optimization and propose a sequential adaptive regularisation using cubics algorithm inspired by sequential quadratic programming (SQP) methods. In each iteration of our method, the … Read more

    An active signature method for constrained abs-linear minimization

  • Timo Kreimeier
  • Andrea Walther
  • Andreas Griewank
    • Categories Nonsmooth Optimization Tags , , , , ,

    In this paper we consider the solution of optimization tasks with a piecewise linear objective function and piecewise linear constraints. First, we state optimality conditions for that class of problems using the abs-linearization approach and prove that they can be verified in polynomial time. Subsequently, we propose an algorithm called Constrained Active Signature Method that … Read more

    Hierarchically constrained blackbox optimization

  • Stéphane Alarie
  • Charles Audet
  • Paulin Jacquot
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization Tags , ,

    In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to define a hierarchical ordering of the constraints and to interrupt the evaluation process at a trial point when it is detected that … Read more

    Constrained Optimization in the Presence of Noise

  • Jorge Nocedal
  • Richard H. Byrd
  • Figen Oztoprak
    • Categories Constrained Nonlinear Optimization Tags , ,

    The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations of the objective and constraint functions. In order to obtain stability, the classical SQP method is modified by relaxing the standard Armijo … Read more

    A Local MM Subspace Method for Solving Constrained Variational Problems in Image Recovery

  • Émilie Chouzenoux
  • Ségolène Martin
  • Jean-Christophe Pesquet
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , , ,

    This article introduces a new Penalized Majorization-Minimization Subspace algorithm (P-MMS) for solving smooth, constrained optimization problems. In short, our approach consists of embedding a subspace algorithm in an inexact exterior penalty procedure. The subspace strategy, combined with a Majoration-Minimization step-size search, takes great advantage of the smoothness of the penalized cost function, while the penalty … Read more