半无限Minimax离散化问题的一个大步长非单调SQP算法

A Large Step Size Non-monotone SQP Algorithm for Semi-infinite Minimax Discretization Problem

针对半无限Minimax的离散化问题,借鉴一般约束优化问题模松弛强次可行SQP算法思想,提出一个求解半无限Minimax离散化问题的非单调SQP算法.算法初始点可以任意选取,通过求解一个QP子问题来得到搜索方向,在非单调线搜索规则的基础上,结合大步长搜索技巧,提出新的大步长非单调线搜索规则来获得下一个迭代点,最后在适当的条件下证明算法的全局收敛性,初步的数值实验验证算法是可行有效的.

For the semi-infinite Minimax discretization problem,a generalized constrained optimization problem model relaxation strong sub-feasible SQP algorithm is proposed. A non-monotonic SQP algorithm for solving the semi-infinite Minimax discretization problem is proposed. The algorithm is characterized in that the initial point can be arbitrarily selected. By solving a QP sub-problem to get the search direction,based on the non-monotone line search rule,combined with the large-step search technique,a new large-step non-monotone line search rule is proposed to obtain the next iterative point,and finally the global convergence of the algorithm is proved under appropriate conditions. The preliminary numerical experimental verification algorithm is feasible and effective.