纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2013年
1期
25-32
,共8页
非线性l1 问题%光滑函数%全局收敛性%算法
非線性l1 問題%光滑函數%全跼收斂性%算法
비선성l1 문제%광활함수%전국수렴성%산법
nonlinear l1 problem%differentiable function%global convergence%algorithm
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.
為非線性l1問題的求解構造瞭光滑逼近函數.首先將非線性l1問題轉化為等價的不可微優化問題;其次通過兩步提齣光滑逼近函數的一般性構造方法;最後進行瞭數值倣真.文中介紹瞭光滑逼近函數的有關性質,指齣相關文獻已有的光滑函數方法是本文的特例,併證明瞭方法的收斂性及有效性.
위비선성l1문제적구해구조료광활핍근함수.수선장비선성l1문제전화위등개적불가미우화문제;기차통과량보제출광활핍근함수적일반성구조방법;최후진행료수치방진.문중개소료광활핍근함수적유관성질,지출상관문헌이유적광활함수방법시본문적특례,병증명료방법적수렴성급유효성.
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.
