NDLI: A New Projection Algorithm for Solving a System of Nonlinear Equations with Convex Constraints

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A New Projection Algorithm for Solving a System of Nonlinear Equations with Convex Constraints

Content Provider	Semantic Scholar
Author	Zheng, Lian
Copyright Year	2013
Abstract	Abstract. We present a new algorithm for solving a system of nonlin-ear equations with convex constraints which combines proximal point andprojection methodologies. Compared with the existing projection meth-ods for solving the problem, we use a diﬀerent system of linear equationsto obtain the proximal point; and moreover, at the step of getting nextiterate, our projection way and projection region are also diﬀerent. Basedon the Armijo-type line search procedure, a new hyperplane is introduced.Using the separate property of hyperplane, the new algorithm is provedto be globally convergent under much weaker assumptions than mono-tone or more generally pseudomonotone. We study the convergence rateof the iterative sequence under very mild error bound conditions. 1. IntroductionLet F : R n → R be a continuous mapping and C ⊂ R n be a nonemptyclosed convex set. Consider the problem of ﬁnding x ∗ ∈ C such that(1) F(x ∗ ) = 0.Let S denote the solution set of problem (1). Throughout this paper, weassume that S is nonempty and F has the property that(2) hF(y),y −x
Starting Page	823
Ending Page	832
Page Count	10
File Format	PDF HTM / HTML
DOI	10.4134/BKMS.2013.50.3.823
Volume Number	50
Alternate Webpage(s)	http://ocean.kisti.re.kr/downfile/volume/kms/E1BMAX/2013/v50n3/E1BMAX_2013_v50n3_823.pdf
Alternate Webpage(s)	https://doi.org/10.4134/BKMS.2013.50.3.823
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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