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Combining pattern search and implicit filtering for solving linearly constrained minimization problems with noisy objective functions

M. A. Diniz-Ehrhardt (cheti***at***ime.unicamp.br)
D. G. Ferreira (deisegema***at***gmail.com)
S. A. Santos (sandra***at***ime.unicamp.br)

Abstract: PSIFA -Pattern Search and Implicit Filtering Algorithm- is a derivative-free algorithm that has been designed for linearly constrained problems with noise in the objective function. It combines some elements of the pattern search approach of Lewis and Torczon (2000) with ideas from the method of implicit filtering of Kelley (2011). The global convergence analysis is presented, encompassing the degenerate case, under mild assumptions. Numerical experiments with linearly constrained problems from the literature were performed. Additionaly, problems with the feasible set defined by polyhedral 3D-cones with several degrees of degeneration at the solution were addressed, including noisy functions that are not covered by the theoretical hypotheses. To put PSIFA in perspective, comparative tests with the Pattern Search and the Implicit Filtering algorithms have been prepared, with encouraging results.

Keywords: Derivative-free optimization; linearly constrained minimization; noisy optimization; global convergence; degenerate constraints; numerical experiments

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

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Entry Submitted: 05/20/2017
Entry Accepted: 05/20/2017
Entry Last Modified: 10/20/2017

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