非线性l1问题的光滑近似算法

摘要

为非线性l1问题的求解构造了光滑逼近函数。首先将非线性l1问题转化为等价的不可微优化问题；其次通过两步提出光滑逼近函数的一般性构造方法；最后进行了数值仿真。文中介绍了光滑逼近函数的有关性质，指出相关文献已有的光滑函数方法是本文的特例，并证明了方法的收敛性及有效性。%A novel smoothing approximation function is constructed to solve nonlinear l1 problem. The model of nonlinear l1 problem is converted to an unconstraint nondifferentiable problem, then the general method of constructing smoothing approximation function is proposed by two steps and finally, numerical examples are given to illustrate the validity of the proposed method. Some properties of approximation functions are presented, and the smooth functions in the existed literatures are pointed out to be the special case of the proposed method in this paper. The convergence of the proposed method is proved.