A stabilized SQP Method: Superlinear Convergence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00307246" target="_blank" >RIV/68407700:21230/16:00307246 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10107-016-1066-7" target="_blank" >https://link.springer.com/article/10.1007/s10107-016-1066-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10107-016-1066-7" target="_blank" >10.1007/s10107-016-1066-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A stabilized SQP Method: Superlinear Convergence

Popis výsledku v původním jazyce

Stabilized sequential quadratic programming (sSQP) methods for nonlinear optimization generate a sequence of iterates with fast local convergence regardless of whether or not the active-constraint gradients are linearly dependent. This paper concerns the local convergence analysis of an sSQP method that uses a line search with a primal-dual augmented Lagrangian merit function to enforce global convergence. The method is provably well-defined and is based on solving a strictly convex quadratic programming subproblem at each iteration. It is shown that the method has superlinear local convergence under assumptions that are no stronger than those required by conventional stabilized SQP methods. The fast local convergence is obtained by allowing a small relaxation of the optimality conditions for the quadratic programming subproblem in the neighborhood of a solution. In the limit, the line search selects the unit step length, which implies that the method does not suffer from the Maratos effect. The analysis indicates that the method has the same strong first- and second-order global convergence properties that have been established for augmented Lagrangian methods, yet is able to transition seamlessly to sSQP with fast local convergence in the neighborhood of a solution. Numerical results on some degenerate problems are reported.

Název v anglickém jazyce

A stabilized SQP Method: Superlinear Convergence

Popis výsledku anglicky

Stabilized sequential quadratic programming (sSQP) methods for nonlinear optimization generate a sequence of iterates with fast local convergence regardless of whether or not the active-constraint gradients are linearly dependent. This paper concerns the local convergence analysis of an sSQP method that uses a line search with a primal-dual augmented Lagrangian merit function to enforce global convergence. The method is provably well-defined and is based on solving a strictly convex quadratic programming subproblem at each iteration. It is shown that the method has superlinear local convergence under assumptions that are no stronger than those required by conventional stabilized SQP methods. The fast local convergence is obtained by allowing a small relaxation of the optimality conditions for the quadratic programming subproblem in the neighborhood of a solution. In the limit, the line search selects the unit step length, which implies that the method does not suffer from the Maratos effect. The analysis indicates that the method has the same strong first- and second-order global convergence properties that have been established for augmented Lagrangian methods, yet is able to transition seamlessly to sSQP with fast local convergence in the neighborhood of a solution. Numerical results on some degenerate problems are reported.

Druh

O - Ostatní výsledky

CEP obor

JC - Počítačový hardware a software

OECD FORD obor

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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

2016

Kód důvěrnosti údajů

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