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2004 | 31 | 2 | 229-242

Tytuł artykułu

On the solution and applications of generalized equations using Newton's method

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Języki publikacji

EN

Abstrakty

EN
We provide local and semilocal convergence results for Newton's method when used to solve generalized equations. Using Lipschitz as well as center-Lipschitz conditions on the operators involved instead of just Lipschitz conditions we show that our Newton-Kantorovich hypotheses are weaker than earlier sufficient conditions for the convergence of Newton's method. In the semilocal case we provide finer error bounds and a better information on the location of the solution. In the local case we can provide a larger convergence radius. Our results apply to generalized equations involving single as well as multivalued operators, which include variational inequalities, nonlinear complementarity problems and nonsmooth convex minimization problems.

Twórcy

  • Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, U.S.A.

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bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-7