半无限规划问题可行方向与离散相结合的算法

A feasible direction method with discretization algorithm for solving semi-infinite optimization

为了得到优化模型中半无限规划问题的局部最优解,结合ZOUTENDIJK可行方向算法以及基于有限覆盖理论基础上的对约束集合离散的算法,给出了一种新的求解半无限规划问题的离散与可行方向结合的算法;并根据择一定理以及一阶最优性充分条件证明了由此新算法得到的迭代点序列能够收敛到半无限规划问题的局部最优解;最后利用此新算法求解了一个半无限规划问题的实例,得到的迭代最优点序列收敛到了最优解,验证了此算法的可行性.

Based on the theories of ZOUTENDIJK feasible direction and finite cover, a new feasible direction with discretization algorithm for acquiring the local optimal solution of semi-infinite programming problems is presented. Meanwhile, the convergence of this algorithm is proved by using the theory of one-order optimal condition. The i＇teration points are testified to be able to accumulate to the local optimal solution too. Finally, the numerical experiment is given by means of an easy example to prove the feasibility of this new algorithm.