非线性规划改进的广义梯度投影法

A Modified Generalized Gradient Projection Algorithm for Nonlinear Programming

关键词:  非线性规划  广义梯度投影  梯度投影  全局收敛性

Key words:  Nonlinear programming  generalized gradient Projection  gradient projection  global converhence

摘要:

讨论带非线性等式和不等式约束规划问题一种新的全局收敛的投影类算法,它是广义梯度投影法和梯度投影法以及次可行方向法的结合和改进.算法具有广义投影阵只依赖于ε-积极约束集,不必计算全部约束函数的梯度,其中ε可以随意选取;由单一的公式给出,且效益函数是可微的等优点.

Abstract:

A new kind of global convergent projection algorithm for programming problems with nonlinear equality and inequality constraints is presented in this paper, it is a combination and modification of generalized gradient and gradient projection as well as subfeasible directions method. The algorithm possesses those main advantages, that is the generalized projection matrices only depend on ε-active constrained set and only a part of the gradient of constrained functions are computed, where ε may be chosen arbitrarily and is given by a single formula; the effective function is differentiable.