用非线性方程组求解等式约束非线性规划问题的降维算法

THE DESCENDING DIMENSION METHOD FOR SOLVING THE NONLINEAR PROGRAMMING PROBLEMS WITH EQUALITY CONSTRAINTS THROUGH A NONLINEAR SYSTEM OF EQUALITY

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.

The descending dimension method is studied for the nonlinear programming problems with linear and nonlinear equality constraints. Firstly, by using of the descending algorithm for the general equality constraints problems, the nonlinear progrrnming problems with only linear equality constraints are transformed into a nonlinear system of equation. And then the solution of the nonlinear programming problems is gained by solving the nonlinear system of equations. Secondly, for the nonlinear propramming problems containing both the linear and nonlinear equality constraints, augmented Lagrange function is constituted by nonlinear constraints and objective ftmction by use of adopting augment Lagrange multiplier method, and the linear eqution constraints are retained. Consequently, a sequence of nonlinear programming problems with only linear equality constraints is obtained, and then they are transformed into the nonlinear programming problems with only linear equality constraints.