解非线性约束拟凸规划的一个梯度投影法

目前国内外所流行的梯度投影法(包括Rosen的原有算法和一些修正算法)还存在以下几个问题:一、要增加Polak程序以保证算法的收僉性。二、在计算投影梯度时,每步一般要作两次投影。三、对于非线性约束问题,负梯度投影方向是不可行的,因此必须在此方向的基础上构造出能保证算法收歛的新可行下降方向。而目前为构造出这个新方向所作的计算都比较复杂。 1981年5]提出了一个处理线性约束条件的梯度投影法,基本上解决了线

A Gradient Projection Method for Quasiconvex Programming with Nonlinear Constraints

This paper proposes a gradient projection algorithm to hanlde quasiconvex programming with nonlinear constraints. The algorithm not only has avoided Polak's perturbation procedure, but it needs only one gradient projection at each iteration instead of projecting two times as in most of the projection methods; and a simple method for constructing a new improved feasible direction is given, It is proved that the algorithm either terminates at an optimal solution after finitely many steps or it generates a sequence of feasible points whose every limit point is an optimal solution of the original problem.