Iterative Algorithms For Solving F -Complementarity Problem

F-complementary problem ( FCP) is introduced by the classical complementary problem. Which has a wide application background,like optimization problem,elastoplast filed. In this paper,we focus on researching theories and algorithms for solving FCP,such as auxiliary problem principle, optimization problem and fixed-point theory. After proving FCP is equivalent to mixed variational inequality problem,in the first method,we introduce a set of new definitions which are generalizations for montotonicity concepts,we use auxiliary problem principle to solve it,and the convergence criteris is also discussed. At last algorithms for soving sub-problem strong convex programming are also discussed.In the second method, FCP can convert into optimization problem,thus we can use gradient project algorithm. By applying a new strongly convex programming,we define a mapping,which is similar to project operator,then the fixed-point algorithm is used to solve FCP,this method is very simple as compared with others,The convergence criteris is also proofed. This is the main innovation in this paper.