The Finite Identification Of Solutions For Saddle Point Problems

Saddle point problem is used in different areas, such as hydromechanics problems, constrained optimization problems, least squares problem, optimal control problems, image recognition problems and issues related to economics. Iteration method used to saddle point problems becomes research focus gradually. The finite identification of algorithms to solve saddle point problem is important for solving practical problems.Some scholars introduced the notion of weak sharpness to mathematical programming problem and variational inequality problem. Under this condition, the finite convergence of the feasible solution sequence is obtained. There is a close relationship between the finite convergence of the feasible solution sequence and weak sharpness. So it is very important to study the weak sharpness of solution set for saddle point problem.Weak sharp solutions of saddle point problems have an important influence on the finite termination of the algorithm. On the basis of existing research of weak sharpness, we introduce the notion of weak sharpness to saddle point problem, and give necessary and sufficient conditions of the property. Under condition of solution set is weakly sharp, we obtain necessary and sufficient conditions of finite termination of a feasible solution sequence to saddle point problems.Then, the concept of strong non-degeneration and augmented weak sharpness of solution set is introduced to saddle point problems. We discuss the relationship between augmented weak sharpness and weak sharpness, strong non-degeneration under the condition of smooth or non-smooth.