Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization

We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic prog...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 46; no. 2; pp. 347 - 368
Main Authors: Izmailov, A. F., Solodov, M. V.
Format: Journal Article
Language:English
Published: Boston Springer US 01.06.2010
Springer Nature B.V
Subjects:
Computational mathematics
Convex and Discrete Geometry
Lagrange multiplier
Management Science
Mathematical programming
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Quadratic programming
Statistics
Studies
Variational problem
(Stabilized) sequential quadratic programming
Josephy–Newton method
Linearly constrained Lagrangian method
Newton method
Generalized equation
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic convergence under the same assumptions as above, which also gives a new result.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-009-9265-2