Iterative Methods For Solving Implicit Complementarity Problem

Firstly,implicit complementarity problem(Abbr.ICP) is introduced by thebackground of complementarity problems(Abbr.CP). All forms of CP and itsapplication to some optimization problems are discussed. ICP is solved by several means in this paper, such as unconstrained optimization,auxiliary problem principle and fix-point theory. The condition that ensures the localoptimal points to be the solution of ICP is discussed in unconstrained optimization.Under some assumptions, ICP is equivalent to generalized variational inequality(Abbr.GVI). We suggest two classes of iterative methods built on the auxiliaryproblem principle for solving ICP, and study the convergence of these methods. Later,the fix-point theory is used to solve ICP.