利用Fisher函数解约束优化问题的广义梯度投影算法

A Generalized Gradient Projection Algorithm with the Fisher Function for Solving the Constrained Optimization Problem

关键词:  约束优化  梯度投影  罚函数  Fisher函数  全局收敛性

Key words:  constrained optimization  gradient projection  penalty function  Fisher function  global convergence

摘要:

通过引入一个辅助优化问题,将广义投影与罚函数技巧和Fisher函数ϕ(a,b)=√a²+b²-(a+b),a,b∈En的特殊性质:√a²+b²-(a+b)=0⇔a ≥ 0,b ≥ 0,ab=0结合起来,给出处理非线性等式、不等式约束问题的广义梯度投影算法,并证明该算法是全局收敛的.该算法不仅保持文献[6]的优点,而且还扩大了初始点的选择范围.

Abstract:

In this paper, we give a generalized gradient projection algorithm for solving equality and inequality constrained optimization problem by introducing an assistant optimization problem and combining the following three facets:1) generalized projection, 2) the sbill of penalty function, 3) Fisher function ϕ (a, b)=√a²+b²- (a+b), which has its special property:√a²+b²- (a+b)=0⇔a ≥ 0, b ≥ 0, ab=0.Furthermore, we prove that this algorithm is globally convergent.This algorithm preserves not only the advantage of reference[6], but also extends the choice range of initial point.