Research On The Quadratic Programming Alxgorithm

Quadratic programming is a significant branch of operational research,it pro-motes the development of optimization theory.For general functions usually can be replaced by the quadratic functions at the near of the minimum point,the meth-ods for quadratic problems is also the tool of nonlinear constrained optimization problems,so it attaches great importance to make a research on these questions.In this paper,we present two methods for quadratic problem,there are Primal-dual active set method and Infeasible primal-dual active set method.Primal-dual.active set method is mainly applied to solving convex quadratic programming with inequality constraints.It based on a guess on the active set,a primal-dual pair(x,s)is computed that satisfies the first order optimality condition and the comple-mentarity condition.If(x,s)is not feasible,a new active set is determined,and the process is iterated.Sufficient conditions for the iterations to stop in a finite number of steps with an optimal solution are provided.Infeasible primal-dual active set method can be used for convex quadratic programming with general constraints.It is also uses the classic Fletcher active set thought,by solving a finite number of equality constrained quadratic programming to get the solution of general con-strained quadratic problem.However,there is a difference with Fletcher active set method is that this method mainly iterate active set to get the active set of the minima,then obtain the minima.In this paper,these two methods belong to infeasible interior point method,while optimization is received,feasibility also will be reached.Computational expe-riences indicate that this approach is effective,and then the comparison with other closely related methods show the superiority of the method.