NDLI: A stabilized SQP method: superlinear convergence

Content Provider	Springer Nature Link
Author	Robinson, Daniel P. Gill, Philip E. Kungurtsev, Vyacheslav
Copyright Year	2016
Abstract	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.
Ending Page	410
Page Count	42
Starting Page	369
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	163
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-09-12
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Optimal control problems involving ordinary differential equations Direct methods for linear systems and matrix inversion Second-order optimality Mathematical Methods in Physics Sequential quadratic programming Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Augmented Lagrangian Mathematical programming methods Stabilized SQP Primal-dual methods Nonlinear programming SQP methods Optimal control problems involving partial differential equations Combinatorics Methods of nonlinear programming type
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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