In this paper, we discuss the variational inequality problems VIP(X, F), where Fis a strongly monotone function and the convex feasible set X is described by some inequality eonstraints. We present a continuation meth...In this paper, we discuss the variational inequality problems VIP(X, F), where Fis a strongly monotone function and the convex feasible set X is described by some inequality eonstraints. We present a continuation method for VIP(X. F). which solves a sequence ofperturbed variational inequality problems PVIP(X. F, ε. μ) depending on two parameters ε≥ 0and μ＞0. It is worthy to point out that the method will be a feasible point type whenε = 0 and a nonfeasible point type when ε＞0, i.e., it is a combined feasible-nonfeasible point(CFNFP for short) method. We analyse the existence, uniqueness and continuity of the solutionto PVIP(X, F, ε,μ), and prove that any sequence generated by this method converges to theunique solution of VIP(X, F).展开更多
文摘In this paper, we discuss the variational inequality problems VIP(X, F), where Fis a strongly monotone function and the convex feasible set X is described by some inequality eonstraints. We present a continuation method for VIP(X. F). which solves a sequence ofperturbed variational inequality problems PVIP(X. F, ε. μ) depending on two parameters ε≥ 0and μ＞0. It is worthy to point out that the method will be a feasible point type whenε = 0 and a nonfeasible point type when ε＞0, i.e., it is a combined feasible-nonfeasible point(CFNFP for short) method. We analyse the existence, uniqueness and continuity of the solutionto PVIP(X, F, ε,μ), and prove that any sequence generated by this method converges to theunique solution of VIP(X, F).
