article

A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares

Authors:

Nicholas I. M. Gould,

Sven Leyffer,

Philippe L. TointAuthors Info & Claims

SIAM Journal on Optimization, Volume 15, Issue 1

Pages 17 - 38

https://doi.org/10.1137/S1052623403422637

Published: 01 January 2005 Publication History

Abstract

We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. Preliminary numerical experience is presented that shows substantial gains in efficiency over the traditional monotone trust-region approach.

Cited By

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Macêdo MKaras ECosta MRocha A(2020)Filter-based stochastic algorithm for global optimizationJournal of Global Optimization10.1007/s10898-020-00917-977:4(777-805)Online publication date: 1-Aug-2020
https://dl.acm.org/doi/10.1007/s10898-020-00917-9
Costa MRocha AFernandes E(2018)Filter-based DIRECT method for constrained global optimizationJournal of Global Optimization10.1007/s10898-017-0596-871:3(517-536)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10898-017-0596-8
Curtis FRaghunathan A(2017)Solving nearly-separable quadratic optimization problems as nonsmooth equationsComputational Optimization and Applications10.1007/s10589-017-9895-867:2(317-360)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s10589-017-9895-8
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Index Terms

A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
    2. Nonlinear equations
  2. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
        Markov-chain Monte Carlo convergence measures
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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cover image SIAM Journal on Optimization

SIAM Journal on Optimization Volume 15, Issue 1

2005

318 pages

ISSN:1052-6234

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2005

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Cited By

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Macêdo MKaras ECosta MRocha A(2020)Filter-based stochastic algorithm for global optimizationJournal of Global Optimization10.1007/s10898-020-00917-977:4(777-805)Online publication date: 1-Aug-2020
https://dl.acm.org/doi/10.1007/s10898-020-00917-9
Costa MRocha AFernandes E(2018)Filter-based DIRECT method for constrained global optimizationJournal of Global Optimization10.1007/s10898-017-0596-871:3(517-536)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10898-017-0596-8
Curtis FRaghunathan A(2017)Solving nearly-separable quadratic optimization problems as nonsmooth equationsComputational Optimization and Applications10.1007/s10589-017-9895-867:2(317-360)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s10589-017-9895-8
Kimiaei MEsmaeili H(2016)A trust-region approach with novel filter adaptive radius for system of nonlinear equationsNumerical Algorithms10.1007/s11075-016-0126-773:4(999-1016)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s11075-016-0126-7
Zhu X(2015)A feasible filter method for the nearest low-rank correlation matrix problemNumerical Algorithms10.1007/s11075-014-9924-y69:4(763-784)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1007/s11075-014-9924-y
Bidabadi NMahdavi-Amiri N(2014)Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least SquaresJournal of Optimization Theory and Applications10.1007/s10957-013-0438-x162:1(154-190)Online publication date: 1-Jul-2014
https://dl.acm.org/doi/10.1007/s10957-013-0438-x
Rocha ACosta MFernandes E(2014)A filter-based artificial fish swarm algorithm for constrained global optimizationJournal of Global Optimization10.1007/s10898-014-0157-360:2(239-263)Online publication date: 1-Oct-2014
https://dl.acm.org/doi/10.1007/s10898-014-0157-3
Periçaro GRibeiro AKaras E(2013)Global convergence of a general filter algorithm based on an efficiency condition of the stepApplied Mathematics and Computation10.1016/j.amc.2013.03.012219:17(9581-9597)Online publication date: 1-May-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.03.012
Fatemi MMahdavi-Amiri N(2012)A filter trust-region algorithm for unconstrained optimization with strong global convergence propertiesComputational Optimization and Applications10.1007/s10589-011-9411-552:1(239-266)Online publication date: 1-May-2012
https://dl.acm.org/doi/10.1007/s10589-011-9411-5
Gu CZhu D(2011)A non-monotone line search multidimensional filter-SQP method for general nonlinear programmingNumerical Algorithms10.1007/s11075-010-9403-z56:4(537-559)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1007/s11075-010-9403-z
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Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares

A filter trust-region algorithm for unconstrained optimization with strong global convergence properties

Pseudo-Transient Continuation for Nonsmooth Nonlinear Equations

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