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On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions (2009)
| Citations: | 18 - 14 self |
BibTeX
@MISC{Izmailov09onattraction,
author = {A. F. Izmailov and M. V. Solodov},
title = { On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions},
year = {2009}
}
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Abstract
Assuming that the primal part of the sequence generated by a Newtontype (e.g., SQP) method applied to an equality-constrained problem converges to a solution where the constraints are degenerate, we investigate whether the dual part of the sequence is attracted by those Lagrange multipliers which satisfy second-order sufficient condition (SOSC) for optimality, or by those multipliers which violate it. This question is relevant at least for two reasons: one is speed of convergence of standard methods; the other is applicability of some recently proposed approaches for handling degenerate constraints. We show that for the class of damped Newton methods, convergence of the dual sequence to multipliers satisfying SOSC is unlikely to occur. We support our findings by numerical experiments. We also suggest a simple auxiliary procedure for computing multiplier estimates, which does not have this
Keyphrases
newton-type iterates second-order sufficiency condition dual sequence primal part equality-constrained problem converges degenerate constraint standard method damped newton method second-order sufficient condition lagrange multiplier dual part numerical experiment simple auxiliary procedure
