卫星舱布局的半无限优化模型及最优性条件(英文)

A Semi-Infinite Optimization Model for the Layout Problem about a Satellite Module and Its Optimality Conditions

本文以人造卫星仪器舱布局问题为背景,建立了一个半无限优化模型.应用图论、群对集合的作用、轨道等,把该问题分解为有限多个子问题,在每个子问题中克服了关于优化变量的时断时续性质.针对每个子问题分析了模型中各函数的性质,并构造了一个局部等价于子问题的极大极小问题.利用这个极大极小问题及子问题中各函数的方向可微性给出了子问题的一阶最优性条件.

This paper studies the layout problem for a satellite module. A semi-infinite optimization model is presented. The layout problem is partitioned into finite subproblems by using graph theory, the action of group on set, orbits and so on, such that each subproblem overcomes its on-off nature about optimal variable. For every subproblem, the properties of all the functions in the model are analyzed. A minimax problem is constructed that is locally equivalent to each subproblem. By virtue of this minimax problem as well as the directionally differentiable property of the functions in every subproblem, the first-order optimality conditions are obtained.