constrained optimization

Cutting Box Strategy: an algorithmic framework for improving metaheuristics for continuous global optimization

  • Marcia Fampa
  • Wendel Melo
  • Fernanda M. P. Raupp
    • Categories Constrained Nonlinear Optimization, Stochastic Approaches Tags , , ,

    In this work, we present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. … Read more

    A cone-continuity constraint qualification and algorithmic consequences

  • Roberto Andreani
  • José Mario Martínez
  • Alberto Ramos
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Every local minimizer of a smooth constrained optimization problem satisfies the sequential Approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qualifications … Read more

    A Flexible Iterative Solver for Nonconvex, Equality-Constrained Quadratic Subproblems

  • Alp Dener
  • Jason Hicken
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , , ,

    We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed … Read more

    Quadratic regularization projected alternating Barzilai–Borwein method for constrained optimization

  • Yakui Huang
  • Hongwei Liu
  • Sha Zhou
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , ,

    In this paper, based on the regularization techniques and projected gradient strategies, we present a quadratic regularization projected alternating Barzilai–Borwein (QRPABB) method for minimizing differentiable functions on closed convex sets. We show the convergence of the QRPABB method to a constrained stationary point for a nonmonotone line search. When the objective function is convex, we … Read more

    Globally Convergent Evolution Strategies for Constrained Optimization.

  • Youssef Diouane
  • Serge Gratton
  • Luis Nunes Vicente
    • Categories Constrained Nonlinear Optimization Tags , , , , , , ,

    In this work we propose, analyze, and test algorithms for linearly constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, … Read more

    Forward – Backward Greedy Algorithms for Atomic – Norm Regularization

  • Nikhil Rao
  • Stephen Wright
  • Parikshit Shah
    • Categories Convex Optimization, Nonsmooth Optimization Tags , ,

    In many signal processing applications, one aims to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as “atoms” allow us to define “atomic norms” that can be used to construct convex regularizers for the reconstruction problem. Efficient algorithms are available to … Read more

    An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

  • Frank E. Curtis
  • Nicholas I. M. Gould
  • Daniel P. Robinson
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, … Read more

    Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction

  • James Murphy
    • Categories Stochastic Programming Tags , , , , , , ,

    This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this … Read more

    An Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Optimization

  • Frank E. Curtis
  • Travis C. Johnson
  • Daniel P. Robinson
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the … Read more

    Superiorization: An optimization heuristic for medical physics

  • Yair Censor
  • Ran Davidi
  • Edgar Garduño
  • Gabor T. Herman
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , ,

    Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The superiorization methodology is presented as a heuristic solver for a … Read more