A Kind Of Fixed Descending Dimension Algorithm For The Nonlinear Programming And Multi-objective Programming

In this paper, descending algorithms for the constrained nonlinear programming problems are discussed and we offer a new way to research methods of nonlinear programming by that. First of all, on the base of the original descending algorithm, we added accurate one dimension searching method (Newton method) into it and gained a new algorithm for the nonlinear programmign with linear equality constraints. It is a improvement and development of the original decending algorithm. Then,we use this algorithm into other programming problems with equlity constrains, such as nonliear programming problem with nonlinear equlity constrains, multi-objective programming problem with linear equlity constrains, and multi-objective programming problem with general equlity constrains, and we set up series of descending algorithms with researching method. Finally, we spark off a new thinking on the nonlinear single objective and multi-objective programming problems with mixed constrains:using the vax variable,we convert the inequality constrains to the equality ones, and then solve it by the desecnding algorithm with accurate one dimension searching method. Moreover a lot of numerical tests have been given for the new algorithm, comparing with the known algorithms, and the results show satisfying precision, so the algorithm is feasible and effective. What is more, we compared the method of using the difference method to obtain derivative to the method of using the function expression to get derivative,and contrasted the linear weighting method with the quadratic weighting method. Through the discussion of the paper, we can find that the algorithms we established have a wide range of using. It is possible to develop into an all-purpose method.