梯度投影下降算法

考虑具有等式约束的非线性规划问题: min{f(z)|φ(z)=θ},(1.1)其中z是n维欧氏空间E~n中的点,θ表示各个空间的零元.f(·)是由E~n到E~1中的函数,称作目标函数.φ(·)=(φ~1(·)),…,φ~r(·))~T是由E~n到E~r(r

THE GRADIENT PROJECTION DESCENT ALGORITHMS

This paper considers the optimization problems with equality constraints. A newidea for constructing algorithms of the gradient projection type is presented. By meansof this idea, the gradient projection restoration, gradient projection Newton and con-jugate gradient projection restoration algorithms are constructed. For these algor-ithms, we also give the theorems of global convergence and the rates of termination con-vergence.