Numerical Algorithms For Local Saddle Point Problem And A Class Of Minimax Problem

In this paper,we studied the numerical algorithms for the local saddle point problem of unconstrained functions and a class of minimax problem with convex inner level.In Chapter 1,we introduce the research background of local saddle point problem of unconstrained functions,the minimax problem and the main content of this paper.In Chapter 2,we give some preliminary knowledge such as notation,theorems,optimality conditions,and Lagrange multipliers.In Chapter 3,we propose two algorithms for the local saddle point problem.Firstly,an algorithm based on the optimality condition of unconstrained optimization problem is given for solving local saddle points in a given region.Then we propose an algorithm to verify whether a local saddle point is a global saddle point or not.Further,the convergences of two algorithms are analyzed.Finally,the effectiveness of two algorithms is demonstrated by numerical experiments.In Chapter 4,we propose a numerical algorithm for solving the minimax problem whose inner level is convex polynomial optimization problem.Firstly,we transform minimax problem to maximum problem based on the optimality condition of general constrained optimization problem,and then we solve it.Further,the convergence of the algorithm is analyzed.Finally,numerical examples are given to demonstrate the effectiveness of the algorithm.The last part,we make a brief summary and prospect for this paper.