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On the Convergence of Pattern Search Algorithms

Author:

Virginia TorczonAuthors Info & Claims

SIAM Journal on Optimization, Volume 7, Issue 1

Pages 1 - 25

https://doi.org/10.1137/S1052623493250780

Published: 01 January 1997 Publication History

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Abstract

We introduce an abstract definition of pattern search methods for solving nonlinear unconstrained optimization problems. Our definition unifies an important collection of optimization methods that neither compute nor explicitly approximate derivatives. We exploit our characterization of pattern search methods to establish a global convergence theory that does not enforce a notion of sufficient decrease. Our analysis is possible because the iterates of a pattern search method lie on a scaled, translated integer lattice. This allows us to relax the classical requirements on the acceptance of the step, at the expense of stronger conditions on the form of the step, and still guarantee global convergence.

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Ge DLiu JLiu TTan JYe Y(2024)Algorithm 1053: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear OptimizationACM Transactions on Mathematical Software10.1145/369995650:4(1-24)Online publication date: 10-Oct-2024
https://dl.acm.org/doi/10.1145/3699956
Brilli AKimiaei MLiuzzi GLucidi S(2024)Worst Case Complexity Bounds for Linesearch-Type Derivative-Free AlgorithmsJournal of Optimization Theory and Applications10.1007/s10957-024-02519-x203:1(419-454)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10957-024-02519-x
Royer CSohab OVicente L(2024)Full-low evaluation methods for bound and linearly constrained derivative-free optimizationComputational Optimization and Applications10.1007/s10589-024-00596-289:2(279-315)Online publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1007/s10589-024-00596-2
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On the Convergence of Pattern Search Algorithms
1. Information systems
  1. Data management systems
    1. Database administration
2. Theory of computation
  1. Design and analysis of algorithms

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cover image SIAM Journal on Optimization

SIAM Journal on Optimization Volume 7, Issue 1

1997

294 pages

ISSN:1052-6234

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 1997

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Ge DLiu JLiu TTan JYe Y(2024)Algorithm 1053: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear OptimizationACM Transactions on Mathematical Software10.1145/369995650:4(1-24)Online publication date: 10-Oct-2024
https://dl.acm.org/doi/10.1145/3699956
Brilli AKimiaei MLiuzzi GLucidi S(2024)Worst Case Complexity Bounds for Linesearch-Type Derivative-Free AlgorithmsJournal of Optimization Theory and Applications10.1007/s10957-024-02519-x203:1(419-454)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10957-024-02519-x
Royer CSohab OVicente L(2024)Full-low evaluation methods for bound and linearly constrained derivative-free optimizationComputational Optimization and Applications10.1007/s10589-024-00596-289:2(279-315)Online publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1007/s10589-024-00596-2
Lee JViswanath KSharma AGeder JPruessner MZhou BWilliams BChen YNeville J(2023)Data-driven machine learning models for a multi-objective flapping fin unmanned underwater vehicle control systemProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i13.26863(15703-15709)Online publication date: 7-Feb-2023
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Vu LFikl ABodony DDesjardins O(2023)An adjoint method for control of liquid-gas flows using a sharp interface modelJournal of Computational Physics10.1016/j.jcp.2023.112057484:COnline publication date: 1-Jul-2023
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Deng LLiu S(2023)A Novel Hybrid Grasshopper Optimization Algorithm for Numerical and Engineering Optimization ProblemsNeural Processing Letters10.1007/s11063-023-11230-355:7(9851-9905)Online publication date: 1-Dec-2023
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García Palomares U(2023)Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimizationComputational Optimization and Applications10.1007/s10589-023-00469-085:3(821-856)Online publication date: 25-Apr-2023
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Ma KRios LBhosekar ASahinidis NRajagopalan S(2023)Branch-and-Model: a derivative-free global optimization algorithmComputational Optimization and Applications10.1007/s10589-023-00466-385:2(337-367)Online publication date: 31-Mar-2023
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Chen HZhao TQian W(2022)Optimal sensor deployment in complex 3D terrain surfaceProceedings of the 2022 International Conference on Pattern Recognition and Intelligent Systems10.1145/3549179.3549186(36-41)Online publication date: 29-Jul-2022
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Pattern Search Algorithms for Bound Constrained Minimization

On the Convergence of the Multidirectional Search Algorithm

On the Convergence of Asynchronous Parallel Pattern Search

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