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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Successive linear programing approach for solving the nonlinear split feasibility problem
 Journal of nonlinear and convex analysis 15 (2014), No.2, pp.345353 ISSN: 13454773 (Print) ISSN: 18805221 (Online) 

 English 
 Journal Article 
 Fraunhofer ITWM () 
Abstract
The Split Feasibility Problem (SFP), which was introduced by Censor and Elfving, consists of finding a point in a set C in one space such that its image under a linear transformation belongs to another set Q in the other space. This problem was well studied both theoretically and practically as it was also used in practice in the area of IntensityModulated Radiation Therapy (IMRT) treatment planning. Recently Li et. al. extended the SFP to the nonlinear framework. Their algorithm tries to follow the algorithm for the linear case. But, unlike the linear case, the involved proximity function is not necessarily convex. Therefore in order to use BaillonHaddad and Dolidze Theorems, the authors assume convexity in order to prove convergence of the projected gradient method. Since convexity of the proximity function is too restrictive, we consider here a Successive Linear Programing (SLP) approach in order to obtain local optima for the nonconvex case. We also aim to intro duce a nonlinear version of the Split Variational Inequality Problem (SVIP).