Newton-Type Methods for Quasidifferentiable Equations

L. W. Zhang and Z. Q. Xia

Journal of Optimization Theory and Applications, 2001, vol. 108, issue 2, No 11, 439-456

Abstract: Abstract In this paper, we present two Newton-type methods for solving quasidifferentiable equations in the sense of Demyanov and Rubinov (Ref. 1). Method I is well defined and is a natural extension of the classical Newton method, based on a generalized Kakutani fixed-point theorem. Method II is a simplified version and requires less computation than Method I. Under some mild assumptions, we establish a locally quadratic convergent theorem for Method I and prove a semilocal convergence theorem for Method II.

Keywords: nonsmooth equations; quasidifferentiable equations; quasidifferentials; Newton-type methods; Kakutani theorem; Krawczyk operator; semilocal convergence (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1026498519948

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