Convergence analysis of the iterative methods for quasi complementarity problems (original) (raw)

Iterative methods for nonlinear quasi complementarity problems

International Journal of Mathematics and Mathematical Sciences, 1987

In this paper, we consider and study an iterative algorithm for finding the approximate solution of the nonlinear quasi complementarity problem of findingu ϵ k(u)such thatTu ϵ k*(u) and (u−m(u),Tu)=0wheremis a point-to-point mapping,Tis a (nonlinear) continuous mapping from a real Hilbert spaceHinto itself andk*(u)is the polar cone of the convex conek(u)inH. We also discuss the convergence criteria and several special cases, which can be obtained from our main results.

Iterative algorithms for semi-linear quasi complementarity problems

Journal of Mathematical Analysis and Applications, 1990

In this paper, we consider an iterative for a class of quasi complementarity problems of finding UGR" such that g(u)~K(u), (Mu+q)~ K*(u), (x(u), Mu+y) =O, where g is a continuous mapping from R" into itself, MER""", PER", and K*(u) is the polar cone of the convex cone K(u) in R". The algorithms considered in this paper are general and unifying ones, which include many existing algorithms as special cases for solving the complementarity problems. We also study the convergence criteria of the general algorithms.

Iterative methods for a class of complementarity problems

Journal of Mathematical Analysis and Applications, 1988

In this paper, we propose and study an algorithm for a new class of complementarity problems of finding u E R" such that u > 0, Tu + A(u) > 0; (u, Tu + A(u)) = 0, where T is a continuous mapping and A is a nonlinear transformation from R" into itself. It is proved that the approximate solution obtained from the iterative scheme converges to the exact solution. Several special cases are also discussed.

On the local convergence of quasi-Newton methods for nonlinear complementarity problems

Applied Numerical Mathematics, 1999

A family of Least-Change Secant-Update methods for solving nonlinear complementarity problems based on nonsmooth systems of equations is introduced. Local and superlinear convergence results for the algorithms are proved. Two different reformulations of the nonlinear complementarity problem as a nonsmooth system are compared, both from the theoretical and the practical point of view. A global algorithm for solving the nonlinear complementarity problem which uses the algorithms introduced here is also presented. Some numerical experiments show a good performance of this algorithm.

Iterative methods for variational and complementarity problems

Mathematical Programming, 1982

In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.

An (m+1)-step iterative method of convergence order (m+2) for linear complementarity problems

Journal of Applied Mathematics and Computing, 2016

In this paper, we present an (m+1)-step iterative method of convergence order (m+2) for solving linear complementarity problems. The proposed iterative method is simple and easy to construct, and requiring only third Fréchet differentiation. Computational efficiency in its general form is discussed and a comparison between the efficiency of the proposed method and existing ones is made. The performance is tested through numerical experiments on some test problems. Keywords Linear complementarity problem • (m+1)-Step iterative method • (m+2) Order method • Sequence of smooth functions • System of non-linear equations Mathematics Subject Classification 90C33 • 90C05 • 90C30 • 90C51 B Y. EL Foutayeni

Fixed point approach for complementarity problems

Journal of Mathematical Analysis and Applications, 1988

In this paper, we use the fixed point technique to suggest a new unified and general algorithm for computing the approximate solution of a nonlinear complementarity problem of finding u such that u > 0, Tu + A(u) > 0 (u, Tu + A(u)) = 0, where T is a continuous mappping from R" into itself and A is a non-linear transformation from Iw" into itself. This algorithm includes many existing algorithms for complementarity problems as special cases. Convergence properties are also discussed and analyzed. 0 1988 Academic press, hc.

An iterative technique for generalized strongly nonlinear complementarity problems

Applied Mathematics Letters, 1999

In this paper, using the change of variables technique, we establish the equivalence between the generalized strongly nonlinear complementarity problems and the Wiener-Hopf equations, This equivalence is used to suggest a new iterative method for the complementarity problems. We also study the convergence analysis of the iterative method and discuss some special cases.

An iterative scheme for generalized mildly nonlinear complementarity problems

Applied Mathematics Letters, 1999

We use the change of variables technique to establish the equivalence between the generalized mildly nonlinear complementarity problems and the Wiener-Hopf equations. This equivalence is used to suggest a new iteratiX, e method for the complementarity problems. We also study the convergence analysis of the iterative method and discuss some special cases.

Generalized quasi complementarity problems

Journal of Mathematical Analysis and Applications, 1986

In this paper, we consider and study a new unified algorithm for obtaining the approximate solution of the generalized quasi complementarity of finding u E K(u), a closed convex set in R", such that F(u) E K*(u), (u-m(u), F(u))=@ where F is a mapping from R" into itself and K*(u) is the polar cone of K(u) and m is a point-to-point mapping from R" into itself. The algorithm includes, as a special case, many existing algorithms for solving generalized complementarity problems.