A Class Of New Descending Algorithm For Constrained Optimization

In this paper, the descending dimension algorithms for the constrained nonlinear programming are discussed and we offer a new way to research methods of nonlinear programming by that. Firstly, we gain a descending dimension form about K-T condition by using hide function theorem. Based on the theorem, we can transfer equality constraints nonlinear problem into unlimited optimization problem by using least square method. Thus, we introduce a new algorithm for nonlinear optimization problem with equality constraints .It is a development of the descending dimension algorithm. Then, we use this algorithm into other programming problems with equality constraints or inequality constraints. Moreover, a lot of numerical tests have been given for the new algorithm, 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 a new Lagrange descending dimension multiplier method. Finally, we can solve equality constraints multi-objective programming by using linear weighting method and solve inequality constraints multi-objective programming by using main target 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.