Quasi-Newton acceleration for equality-constrained minimization

Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear...

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Bibliographic Details
Published in:Computational optimization and applications 2008-07, Vol.40 (3), p.373-388
Main Authors: Ferreira-Mendonça, L., Lopes, V. L. R., Martínez, J. M.
Format: Article
Language:English
Subjects:
Algorithms
Computer science
Convex and Discrete Geometry
Management Science
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Optimization algorithms
Quadratic programming
Statistical analysis
Statistics
Studies
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Summary:Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this paper quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms, with equality constraints. A periodically-restarted memoryless symmetric rank-one (SR1) correction method is introduced for that purpose. Convergence results are given and numerical experiments that confirm that the acceleration is effective are presented.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-007-9090-4