广义箱子约束优化基于线性逼近子问题的显式搜索方向算法

Algorithm with explicit search directions based on line approximate subproblems for generalized box constrained optimization

讨论带广义箱子约束的非线性约束优化.基于Topkis-Veinott线性规划逼近法,对搜索方向子问题进行改进,产生两个新的线性逼近子问题,重要的是两个新子问题的解均能以简单的显式表达式直接给出.由此建立问题非精确线搜索算法,算法大大降低了计算量,复杂性及CPU时间.仅在目标函数连续可微的条件下,算法具有全局收敛性.对算法进行较大规模的数值试验.

In this paper,optimization with generalized box constraints is discussed.First,based on the Topkis-Veinott＇s line program approximate method,two improved direction finding subproblems （DFS） are introduced,and the more important thing is that the optimal solution of the DFS can be obtained by an explicit formula.Then,an algorithm for the discussed optimization is proposed based on the new DFS.The computation cost and complexity as well as CPU time of the proposed algorithm are decreased largely.The global convergence is proved just under the continuous differentiability of the objective function.Finally,numerical experiments on some slight large scale testing problems are reported.