The Descending Dimension Algorithm By A Nonlinear System Of Equations Of The Programming Problems With Equality Constraints

In this thesis, the descending dimension algorithm for the nonlinear programming and multi-objective programming problems with equality constraints is discussed. The nonlinear programming problems with only linear equation constraints, by using the descending dimension form of the K-T condition, can be transformed into a nonlinear system of equations. And then the solution of the nonlinear programming problems is gained by solving the nonlinear system of equations (algorithm 1). For the nonlinear programming problem containing both the linear and nonlinear equality constrained, augmented Lagrange function is constituted by nonlinear constraints and objective function by use of adopting augment Lagrange multiplier method, and the linear equation constraints are retained. Consequently, a sequence of nonlinear programming problems with only linear equality constraints is obtained. Thus, the problem is transformed into the nonlinear programming problems with only linear equality constraints (algorithm 2). For multi-objective programming problems with only linear equality constrains, or multi-objective programming problems with linear and nonlinear equality constrains, the multi-objective programming problems can be transformed into a nonlinear programming problems with only linear equation constraints or with linear and nonlinear equation constraints by using the linear weighting, and the solutions of the multi-objective programming problems are solved by adopting the algorithm 1 or the algorithm 2 (algorithm 3), (algorithm 4). Finally,compared with the results calculated by Matlab Optimization Toolbox, the numerical experiment given show the feasibility and effectiveness of the descending dimension algorithm.