A stabilized SQP Method: Global Convergence

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00307245" target="_blank" >RIV/68407700:21230/17:00307245 - isvavai.cz</a>

Result on the web

<a href="https://academic.oup.com/imajna/article-abstract/37/1/407/2669936/A-stabilized-SQP-method-global-convergence" target="_blank" >https://academic.oup.com/imajna/article-abstract/37/1/407/2669936/A-stabilized-SQP-method-global-convergence</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/imanum/drw004" target="_blank" >10.1093/imanum/drw004</a>

Result language

angličtina

Original language name

A stabilized SQP Method: Global Convergence

Original language description

Stabilized sequential quadratic programming (SQP) methods for nonlinear optimization are designed to provide a sequence of iterates with fast local convergence even when the active-constraint gradients are linearly dependent. This paper concerns the global convergence properties of a stabilized SQP method with a primal–dual augmented Lagrangian merit function. The proposed method incorporates two novel features. First, a flexible line search is used based on a direction formed from an approximate solution of a strictly convex quadratic programming (QP) subproblem and, when one exists, a direction of negative curvature for the primal–dual merit function. Second, when certain conditions hold, an approximate QP solution is computed by solving a single linear system defined in terms of an estimate of the optimal active set. We also establish two desirable convergence results. (i) It is shown that with an appropriate choice of termination condition, the method terminates in a finite number of iterations without the assumption of a constraint qualification. The method may be interpreted as an SQP method with an augmented Lagrangian safeguarding strategy. This safeguarding becomes relevant only when the iterates are converging to an infeasible stationary point of the norm of the constraint violations. Otherwise, the method terminates with a point that approximately satisfies certain second-order necessary conditions for optimality. In this situation, if all termination conditions are removed, then the limit points either satisfy the same second-order necessary conditions exactly or fail to satisfy a weak second-order constraint qualification. (ii) The global convergence analysis concerns a specific algorithm that estimates the least curvature of the merit function at each step. If negative curvature directions are omitted, the analysis still applies and establishes convergence to either first-order solutions or infeasible stationary points.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/EE2.3.30.0034" target="_blank" >EE2.3.30.0034: Support of inter-sectoral mobility and quality enhancement of research teams at Czech Technical University in Prague</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

IMA Journal of Numerical Analysis (IMAJNA)

ISSN

0272-4979

e-ISSN

1464-3642

Volume of the periodical

37

Issue of the periodical within the volume

1

Country of publishing house

GB - UNITED KINGDOM

Number of pages

37

Pages from-to

407-443

UT code for WoS article

000397147700014

EID of the result in the Scopus database

2-s2.0-85017019334