一主多从两层非光滑优化问题的集成算法

Integrated Algorithm for Bilevel Nonsmooth Optimization Problems

对于一类一主多从两层非光滑优化问题，提出了将置信域束法和变尺度法结合起来的一种集成算法．该算法能自适应地将变尺度法嵌入到束法的内部迭代中去，从而能够充分利用束法的全局收敛性和变尺度法的快速收敛速度．研究了模型构成函数的Ｌｉｐｓｃｈｉｔｚｉａｎ性，给出了计算目标函数次梯度的方法，分析了算法思想、步骤。

This paper is concerned with a kind of 1 leader N followers bilevel nonsmooth optimization problems. An integrated algorithm is proposed which embeds adaptively DFP into the inner iteration of the trust region bundle method and makes the best use of the global convergence of the bundle method and the local fast convergence of the DFP. The Lipschitzian property of functions involved is researched. An approach of computing a subgradient of the objective functions of the problems is investigated. The basic idea and steps of the algorithm are discussed. Finally, the convergence analysis is given.