初始点任意优化问题的广义梯度投影法

A General Gradient Projection Method with Arbitrary Initial Point for Optimization Problems

利用广义投影与罚函数技巧和辅助规划处理带等式和不等式约束问题以及采用二阶段搜索方法，给出了一个初始点可任意的带不等式和等式约束的优化问题的广义梯度投影算法，并证明了该算法具有全局收敛性。文中削弱了文献［１］的条件，保持了它的优越性，罚参数在计算过程中自动调整且只需适当大，因此，在实际运用中不会有太大的困难。

This paper combines generalized projection matrix with penalty function technique. The auxiliary programming is used to deal with inequality and equality constraint and a two stage search method is used to give a method with arbitrary initial point for nolinear equality and inequality constrained optimization problems,while this algorithm is global convergence. This paper weakens condition in Ref. [2]and maintains it's priority, parameter of penalty automatic adjust and only need proper large in the calculating process,thereforce,it is unlikely to produce more difficulty in practice.