A Descending Algorithm For The Constrained Nonlinear Programming Problem

In this thesis, a descending algorithm for the constrained nonlinear programming problem and applications of the optimization method in factual problems are discussed, and we offer a new way to research methods of nonlinear programming by that. Firstly, we get the K-T point of the nonlinear programming problem with equal constrains by solving an equations by the descending form of the Kuhn-Tucker condition, and the descending algorithm for the optimization problem with equal constrains is consummated; Secondly, on the basis of the descending algorithm, it separately offer the descending algorithm for the general nonlinear programming with unequal constrains and the nonlinear programming with linear constrains combined with active-set strategy. Else, the convergence of these algorithms is also discussed, and the convergence results under certain conditions are given. Considering that there are no general algorithms for the nonlinear programming problem, the discussion in this part offer a new way to research it. Thirdly, 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. Finally, we set up the optimization models for engineering design and portfolio allocation and solve them, thereinto we solve the latter by both the descending algorithm and SQP, so the application of optimization methods in factual problems are researched in certain deepness.