The convergence rates for the regularized solutions is also shown under ordinary conditions in the theory of nonlinear ill-posed problems. We also give a numerical example as an illustration. | JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci. 2014 Vol. 59 No. 7 pp. 44-51 This paper is available online at http ABOVE REGULARIZATION FOR CONSTRAINED GENERALIZED COMPLEMENTARITY PROBLEMS Nguyen Thi Thuy Hoa1 and Nguyen Buong2 1 Informatics Center Hanoi University of Home Affairs 2 Institute of Information Technology Vietnamese Academy of Science and Technology Abstract. The purpose of this paper is to use the Tikhonov regularization method to solve a constrained generalized complementarity problems that is to find an element x C g x 0 h x 0 g x h x Em 0 where C is a convex n closed subset in E g x and h x are two continuous functions from an Euclidian space En to Em and . . En denotes the scalar product of En . The convergence rates for the regularized solutions is also shown under ordinary conditions in the theory of nonlinear ill-posed problems. We also give a numerical example as an illustration. Keywords Convex set Tikhonov regularization continuous function. 1. Introduction Let g x and h x be two continuous functions from an Euclidian space En to Em where the scalar product and norm of En are denoted by . . En and . En respectively. The problem of finding an element x En such that x 0 h g x 0 g x h x Em 0 where the symbol y y1 . ym 0 is meant that yi 0 i 1 . m is called a generalized complementarity problem GCP . In the case that m n g x x and h x F x a continuous function in En is the classical nonlinear complementarity problem NCP we find an element x En satisfying x 0 F x 0 x F x En 0 Received September 12 2014. Accepted October 23 2014. Contact Nguyen Thi Thuy Hoa e-mail address nguyenhoanvhn@ 44 Above regularization for constrained generalized complementarity problems which has attracted much attention due to its various applications see 6 8 10 . There exist several methods for the solution of the NCP 3 4 7 . All of these methods are proposed for solving an equivalent minimization problem or a system of .
