Lipschitz函数全局优化的区间算法  

An Interval Algorithm for Lipschitz Global Optimization

作　　者：孙靖[1] 曹德欣[1] 

机构地区：[1]中国矿业大学理学院

出　　处：《中国矿业大学学报》2007年第5期711-716,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(60575046);中国矿业大学科技基金项目(A200410);淮海工学院科研基金项目(Z2004029)

摘　　要：利用广义梯度讨论了目标函数是Lipschitz连续的非光滑优化问题的区间算法,给出了求二维函数广义梯度的区间算法,提出了利用广义梯度估计Lipschitz常数的方法.定理和数值算例表明,通过随算法的进行而不断修正Lipschitz常数,算法的收敛速度得到了一定的提高.An interval algorithm for solving a nonsmooth optimization was discussed, whose objective function is Lipschitz continuous by generalized gradient. An interval algorithm for computing generalized gradient of two-dimension function and a method for estimating Lipschitz constant by generalized gradient were given . The theory and numerical results show that the convergent speed of the algorithm is improved due to updating the Lipschitz constant with the algorithm proceeding.

关 键 词：非光滑优化问题 区间算法 广义梯度 

分 类 号：O221.4[理学—运筹学与控制论]