Rates of convergence of Newton type methods for variational inequalities and nonlinear programming

Abstract : This paper presents some new results in the theory of Newton type methods for variational inequalities and their application to nonlinear programming. A condition of semi-stability is shown to ensure the quadratic convergence of Newton's method and the superlinear convergence of some quasi-Newton algorithms, provided the sequence defined by the algorithm exists and converges. A partial extension of these results to nonsmooth function is given. The second part of the paper considers some particular variationnal inequalities with unknowns {x, l) generalizing optimality systems. Here only the question of superlinear convergence of {xk} is considered. Some necessary or sufficient conditions are given. Applied to some quasi-Newton algorithms they allow to obtain the superlinear convergence of {xk}. The application of the previous results to nonlinear programming allows to strenghten the know results, the main point being a characterization of the superlinear convergence of {xk} assuming a weak second-order condition without strict complementary.
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Rapport
[Research Report] RR-1260, INRIA. 1990
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https://hal.inria.fr/inria-00075298
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Dernière modification le : vendredi 16 septembre 2016 - 15:11:33
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J. Frederic Bonnans. Rates of convergence of Newton type methods for variational inequalities and nonlinear programming. [Research Report] RR-1260, INRIA. 1990. 〈inria-00075298〉

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