非线性不等式组的信赖域算法  

Trust Region Method for Nonlinear Inequalities

作　　者：何郁波[1] 马昌凤[2] 

机构地区：[1]怀化学院数学系,怀化418008 [2]桂林电子科技大学数学与计算科学学院,桂林541004

出　　处：《工程数学学报》2008年第2期224-230,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10661005);广西自然科学基金(0640165)．

摘　　要：对于非线性不等式组的求解,采用构造辅助函数将非线性不等式组转化成为一个非线性方程组。文中采用光滑信赖域方法对非线性方程组进行逐次逼近从而求得问题的解。算法的全局收敛性和局部超线性收敛性得到了保证,数值试验表明算法对于小规模问题是切实可行的。Based on a new smooth function, we reformulate nonlinear inequalities as a nonsmooth equation. Then a successive approximation trust region method for solving the minimization problem is proposed and the global convergence of the method is established. In addition, it is verified that the method is also superlinearly convergent under the suitable condition. Numerical results show that our algorithm performs well for the small-scale nonlinear inequalities.

关 键 词：非线性不等式组 信赖域方法 逐次近似 全局收敛 局部超线性收敛 

分 类 号：O178.2[理学—数学]