Quasi-Newton acceleration for equality-constrained minimization |
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Authors: | L Ferreira-Mendonça V L R Lopes J M Martínez |
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Institution: | 1.Department of Computer Science, IM-UFRJ,Federal University of Rio de Janeiro,Rio de Janeiro,Brazil;2.Department of Applied Mathematics, IMECC-UNICAMP,University of Campinas,Campinas,Brazil |
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Abstract: | 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.
This work was supported by FAPESP, CNPq, PRONEX-Optimization (CNPq / FAPERJ), FAEPEX, UNICAMP. |
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Keywords: | Optimality systems Quasi-Newton methods Minimization with equality constraints |
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