一般约束优化问题的摄动梯度投影法

利用梯度投影法与罚函数技巧,将带等式和不等式约束优化问题化成一个无约束问题,提出了求解不等式、等式约束优化问题的摄动梯度投影算法。考虑到计算的误差因素,在搜索方向上进行摄动,得到一个方向不精确的梯度投影法。参数Wk取不同的数还可以得到一类梯度投影法。从而保证了在实际应用中更容易实现,在较弱的条件下,证明了该算法的全局收敛性。

A Perturbed Gradient Projection Method for General Constrained Optimization Problems

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 Wk is differently chosed.The algorithm is globally convergent under very weak conditions.