CONSTRAINED OPTIMIZATION IN THE PRESENCE OF NOISE

Figen Oztoprak; Richard Byrd; Jorge Nocedal

doi:10.1137/21M1450999

CONSTRAINED OPTIMIZATION IN THE PRESENCE OF NOISE

Figen Oztoprak, Richard Byrd, Jorge Nocedal

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 line search based on the noise level in the functions, which is assumed to be known. Convergence theory is presented giving conditions under which the iterates converge to a neighborhood of the solution characterized by the noise level and the problem conditioning. The analysis assumes that the SQP algorithm does not require regularization or trust regions. Numerical experiments indicate that the relaxed line search improves the practical performance of the method on problems involving uniformly distributed noise, compared to a standard line search.

Original language	English (US)
Pages (from-to)	2118-2136
Number of pages	19
Journal	SIAM Journal on Optimization
Volume	33
Issue number	3
DOIs	https://doi.org/10.1137/21M1450999
State	Published - 2023

Funding

*Received by the editors October 6, 2021; accepted for publication (in revised form) March 10, 2023; published electronically August 10, 2023. https://doi.org/10.1137/21M1450999 Funding: The third author was supported by National Science Foundation grant DMS-2011494, AFOSR grant FA95502110084, and ONR grant N00014-21-1-2675. \dagger Department of Industrial Engineering, Gebze Technical University, Turkey and Artelys Corporation, Chicago, IL 60601 USA ([email protected]). \ddagger Computer Science Department, University of Colorado, Boulder, CO 80309 USA (richardhbyrd@ gmail.com). \S Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60201 USA ([email protected]).

Keywords

constrained optimization
noisy optimization
nonlinear optimization

ASJC Scopus subject areas

Software
Theoretical Computer Science
Applied Mathematics

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10.1137/21M1450999

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abstract = "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 line search based on the noise level in the functions, which is assumed to be known. Convergence theory is presented giving conditions under which the iterates converge to a neighborhood of the solution characterized by the noise level and the problem conditioning. The analysis assumes that the SQP algorithm does not require regularization or trust regions. Numerical experiments indicate that the relaxed line search improves the practical performance of the method on problems involving uniformly distributed noise, compared to a standard line search.",

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AB - 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 line search based on the noise level in the functions, which is assumed to be known. Convergence theory is presented giving conditions under which the iterates converge to a neighborhood of the solution characterized by the noise level and the problem conditioning. The analysis assumes that the SQP algorithm does not require regularization or trust regions. Numerical experiments indicate that the relaxed line search improves the practical performance of the method on problems involving uniformly distributed noise, compared to a standard line search.

KW - constrained optimization

KW - noisy optimization

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CONSTRAINED OPTIMIZATION IN THE PRESENCE OF NOISE

Abstract

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Keywords

ASJC Scopus subject areas

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