Existence Theorems And Projection Algorithms For F-Complementarity Problem

As a crossover research field of operational research and computational mathematics,complementary problem is closely linked with game theory, optimization, the fixed point theory andthe minimax problem. It has been widely used in economics, mechanics, transportation andengineering departments. At the same time, along with the development of the theory and practice,there is a complementary problem with more extensive application: F-complementarity problem(FCP). It has a wide application background, like optimization problem, elastoplasts field. BecauseFCP is the extension of the classic complementary problem, so study the theory and algorithm ofFCP is greatly to unite the theory and algorithm of the classic complementary problem.In this paper, we study the existence theorems and projection algorithms for F-complementarity problem. First, by using some lemmas, we obtain the existence theorems ofFVIP and FCP under some assumptions with the equivalence between FVIP and FCP. Second, weuse a kind of projection operator to transfer FCP into an iterative equation and solve it with theproximal point algorithm; also we prove the convergence of the algorithm. At last, we transfer themonotone FCP into the classic variational inequality problem by defining a new mapping and solveit with the projection and contraction method; also we prove the convergence of the algorithm undersome assumptions. This is the main innovation in this paper.