受凝聚映象扰动的极大增生算子的拓扑度

A Perturbed Gradient Projection Method for General Constrained Optimization Problems

拓扑度理论对于研究算子方程解的存在性、唯一性、连续依赖性等问题具有重要的理论价值［１］。文献［２，３］利用拓扑度方法探讨了一般算子方程ｙ∈（Ａ＋Ｃ）ｘ解的问题，文中在此基础上给出了极大增生算子Ａ受凝聚映象Ｃ扰动时的拓扑度。

In this paper,the gradient projection and penalty function are used to make optimization problems for inequality and equality constraints into optimization problems without constraints.An algorithm of perturbed gradient projection for inequality and equality constrained problems is given.Considering the error of calculating and perturbing in search direction,a gradient projection method for inexact search direction is produced,which can get a sort of gradient projection algorithm when parameter δ k is differently chosed.The algorithm is globally convergent under very weak conditions.