A stabilized SQP Method: Global Convergence

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A stabilized SQP Method: Global Convergence

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A stabilized SQP Method: Global Convergence

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/EE2.3.30.0034" target="_blank" >EE2.3.30.0034: Podpora zkvalitnění týmů výzkumu a vývoje a rozvoj intersektorální mobility na ČVUT v Praze</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

IMA Journal of Numerical Analysis (IMAJNA)

ISSN

0272-4979

e-ISSN

1464-3642

Svazek periodika

37

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

37

Strana od-do

407-443

Kód UT WoS článku

000397147700014

EID výsledku v databázi Scopus

2-s2.0-85017019334