Iterative Algorithms For Solving A Class Of F-complementarity Problem

F-complementarity problem is produced by the classical complementarity problem and thefunction disturbance, which comes from optimization theory and has a wide application background,being widely used in optimization problem and elastoplast filed. Because F-complementarity problemis the extension of classical complementarity problem, studying the theory and algorithm ofF-complementarity problem is greatly to unite the theory and algorithm of the classicalcomplementarity problem.In this paper, some algorithms for a form of F-complementarity problem are designed. First, oncondition of the equivalence of F-complementarity problem and mixed variational inequality problem,the equivalence of mixed variational inequality problem and optimization problem, by using thedefinition of limit and Bregman function to establish the equivalence of F-complementarity problemand a generalized variational inequality when the disturbance function is smooth, then a near pointalgorithm of this form of F-complementarity problem with convergence is discussed and theequivalence of complementarity problem and this variational inequality problem in convexpolyhedron is proved. Second, a optimal condition of F-complementarity problem is proposed whenthe disturbance function is nonsmooth, then subgradient is offered and it’s convergence is proved. Atlast, a predictor-corrector algorithm for solving F-complementarity problem is designed and itsfeasibility and convergence is proved, then a numerical example shows the effectiveness of thisalgorithm.