A stabilized SQP Method: Superlinear Convergence

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

A stabilized SQP Method: Superlinear Convergence

Original language description

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.

Czech name

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Czech description

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Type

O - Miscellaneous

CEP classification

JC - Computer hardware and software

OECD FORD branch

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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

2016

Confidentiality

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