约束优化问题的一个超线性收敛的广义梯度投影法

A Superlinearly Convergent Generalized Gradient Projection Method for Linearly Constrained Optimization Problem

对线性约束的非线性优化问题提出了一个新的广义梯度投影法 ,该算法我们采用了非精确线性搜索 ,并在每次迭代运算中运用了广义投影矩阵和变尺度方法的思想确定其搜索方向。在通常的假设条件下 。

In this paper, a new generalized gradient projection method is proposed for the nonlinear optimization problem with linear constraints. The generalized projection matrix and the variable metric method idea are used to determine the search direction at each iteration. It is proved that, under some suitable assumption, the method using the inexact line search has properties of global convergence and superlinear convergence rate.