A Kantorovich-type convergence analysis of the Newton---Josephy method for solving variational inequalities

Authors:
Ioannis K. Argyros;Saïd Hilout
Affiliations:
Department of Mathematics Sciences, Cameron University, Lawton, USA 73505;Laboratoire de Mathématiques et Applications, Poitiers University, Futuroscope Chasseneuil Cedex, France 86962
Venue:
Numerical Algorithms
Year:
2010

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Abstract

We present a Kantorovich-type semilocal convergence analysis of the Newton---Josephy method for solving a certain class of variational inequalities. By using a combination of Lipschitz and center-Lipschitz conditions, and our new idea of recurrent functions, we provide an analysis with the following advantages over the earlier works (Wang 2009, Wang and Shen, Appl Math Mech 25:1291---1297, 2004) (under the same or less computational cost): weaker sufficient convergence conditions, larger convergence domain, finer error bounds on the distances involved, and an at least as precise information on the location of the solution.