Lagrange Descending Dimension Multiplier Method For Non-linear Programming Problem With Linear And Non-linear Constraints

In this paper, the descending dimension algorithm for nonlinear programming problems with linear equality constraints are discussed. Firstly, we gain a descending dimension form about K-T condition by using hide function theorem. Based on the theorem, using some knowledge about submatric , a more efficient algorithm(algorithm 1) for quadratic programming with linear equality constraints is gained. Secondly, nonlinear programming problem with linear equality constraints is presented, and it is become a series of quadratic programming problems with linear equality constraints by the series quadratic programming method, and then every quadratic programming problems is solved by the first algorithm. The algorithm(algorithm 2) is proved second-order convergence. Thirdly, by using augment Lagrange multiplier method, we change nonlinear programming problem with linear equality and linear equality constraints into nonlinear programming problem only with linear equality constraints. Because algorithm for sub-problem is second-order convergence, this algorithm (algorithm 4) converge rapidly. I particularly points out that this descending dimension Lagrange multiplier algorithm improves penalty function algorithm and advance accuracy to a certain degree. Finally, nonlinear programming problem with linear and nonlinear equality and nonlinear inequality constraints is introduced. Changing it's inequality constraints into equality constraints, the question is changed nonlinear programming problem with linear and nonlinear equality constraints and solved. Numerical experiment shows these methods are effective.