Numerical Algorithms On Saddle Point Problem Of Rational Function And A Class Of Nonlinear Programming

Polynomial optimization problem is a class of optimization problem with special structure and wide application.In recent years,many scholars have studied its global optimization method.In this paper,the numerical algorithms of the saddle point problem of rational functions and a class of nonlinear programming with complex structure are studied by using the classical theory and algorithm of polynomial optimization.For the saddle point problem of rational functions,based on the optimality condition and Lasserre relaxation method,a numerical algorithm for the saddle point problem of rational functions is proposed by using the method solving polynomial saddle point problem.The algorithm can judge whether there are saddle points in rational functions and get saddle points if there are saddle points.Numerical results show that this method is feasible.The algorithm can be used to solve the saddle point problem of rational functions where the objective function is not convex or concave or the constraint set is not convex.For nonlinear programming with complex structure,first of all,the problem is transformed into polynomial optimization problem by using variable substitution.Then,Lasserre relaxation method is applied to solve the optimization problem of polynomials,and its approximative global optimal solution can be gotten.After that,approximative solution of the original nonlinear programming can be obtained by using inverse substitution.The convergence of the algorithm is proved.At last,the numerical results show that the algorithm is effective.Finally,we make a brief summary and prospect for this paper.