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

• Autorzy: Ioannis K. Argyros
• 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.

Kategorie tematyczne

• 49M15: Newton-type methods
• 65G99: None of the above, but in this section
• 65J15: Equations with nonlinear operators (do not use )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2004
• Tom: 31
• Numer: 2
• Strony: 229-242

Daty

wydano

2004

Twórcy

autor

Ioannis K. Argyros

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

Identyfikatory

DOI

10.4064/am31-2-7