A New Algorithm For The Linear Constrained Nonlinear Programming Problem

In this thesis, A descending algorithm for the constrained nonlinear programming problem and applications of the optimization method in factual are discussed based on the descending dimension form of the K-T condition, which is discovered by professor Li Ze-min and we offer a new way to research methods of nonlinear programming by that.The thought which the article research is that : Firstly we research the quadratic problem with the linear equality constraint and solve the quadratic problem with the linear unequality constraint by sequence programming method and active —set strategy.Secondly we research the problem that its object function is a general nonlinear function. Then, we use the second order form of Taylor expansion to approach the single objective function so that we can get a quadratic program problem.Numerical tests are given for every kind of the descending algorithm,comparing with the known algorithms,the results show satisfying precision,so the algorithm is feasible and effective.Besides in this paper the convergence of these algorithms is also discussed,and the convergence results under certain conditions are given and proved. Finally, The article shows application of these algorithm in supply chain management. That is , Production planning for supply chain based on integration of production, provision and distribution is studied and a multi-objective optimization model is proposed.On the one hand,The results show value of these algorithms in economy.On the other hand it proves validity of the these algorithms and perfects research to the descending algorithm.