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

通过引入一个辅助优化问题,将广义投影与罚函数技巧和F isher函数(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.

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 shill of penalty function, 3） Fisher function φ（a,b）=√a^2＋b^2-（a＋b）, which has its special property： √a^2＋b^2（a＋6）=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.