线性半无限规划的梯度投影法

The gradient projection method of linear semi-infinite programming

考虑在实线性空间中一类变量个数有限而指标个数无限,具有解析系统的线性半无限规划(LSIP)问题.通过研究当前迭代点与可行域的关系、积极梯度集、可行下降方向以及迭代步长,得到了几个理论结果,提出了一个求解LSIP问题的投影梯度法,证明了理论的正确性,最后通过数值实例验证了该算法的实际可行性.

A class of the continuous linear semi -infinite programming problems was considened, with finite number of variables and infinitely constraints index set over a compact metric space. The relationship was investigated between current iteration point and the feasible region, and the active gradient set, feasible descent direction and iteration step size, were discussed, and then some theoretical results were obtained. And then a gradient project method for solving semi - infinite programming problems is presented. In the end , Several numerical examples illustrating the algorithm practical are given, these numerical results are in excellent agreement with theoretical analysis.