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A Sequential Quadratic Programming Algorithm for Equality-Constrained Optimization without Derivatives

Tröltzsch, Anke (2016) A Sequential Quadratic Programming Algorithm for Equality-Constrained Optimization without Derivatives. Optimization Letters, 10 (2), pp. 383-399. Springer. DOI: 10.1007/s11590-014-0830-y ISSN 1862-4472

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Official URL: http://link.springer.com/article/10.1007/s11590-014-0830-y


In this paper, we present a new model-based trust-region derivative-free optimization algorithm which can handle nonlinear equality constraints by applying a sequential quadratic programming (SQP) approach. The SQP methodology is one of the best known and most efficient frameworks to solve equality-constrained optimization problems in gradient-based optimization. Our derivative-free optimization (DFO) algorithm constructs local polynomial interpolation-based models of the objective and constraint functions and computes steps by solving QP sub-problems inside a region using the standard trust-region methodology. As it is crucial for such model-based methods to maintain a good geometry of the set of interpolation points, our algorithm exploits a self-correcting property of the interpolation set geometry. To deal with the trust-region constraint which is intrinsic to the approach of self-correcting geometry, the method of Byrd and Omojokun is applied. Numerical experiments are carried out on a set of test problems from the CUTEr library and on a simulation-based engineering design problem.

Item URL in elib:https://elib.dlr.de/102926/
Document Type:Article
Title:A Sequential Quadratic Programming Algorithm for Equality-Constrained Optimization without Derivatives
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Tröltzsch, Ankeanke.troeltzsch (at) dlr.deUNSPECIFIED
Date:February 2016
Journal or Publication Title:Optimization Letters
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1007/s11590-014-0830-y
Page Range:pp. 383-399
Krokhmal, PavloUniversity of Iowa
Prokopyev, Oleg A.University of Pittsburgh
Keywords:derivative-free optimization, nonlinear optimization, trust region, DFO, SQP
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transport
DLR - Research area:Raumfahrt
DLR - Program:R RP - Raumtransport
DLR - Research theme (Project):R - Proj. Thermas (old), R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > Distributed Systems and Component Software
Institut of Simulation and Software Technology
Deposited By: Tröltzsch, Anke
Deposited On:08 Aug 2016 10:02
Last Modified:06 Sep 2019 15:30

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