南京师大学报(自然科学版)
南京師大學報(自然科學版)
남경사대학보(자연과학판)
JOURNAL OF NANJING NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2013年
2期
31-38
,共8页
不可微%l1问题%内点算法%盒式约束最小二乘问题
不可微%l1問題%內點算法%盒式約束最小二乘問題
불가미%l1문제%내점산법%합식약속최소이승문제
nondifferentiable%l1 problem%interior point algorithm%quadratic programming problem with box constrains
本文对非线性l1问题minx∈RnF( x)=∑m i=1|fi(x)|,从理论上研究了F(x)的下降方向、最优解与某种盒式约束最小二乘问题的最优解之间的关系,进而构造了一个非线性l1问题的下降算法,并证明了该算法的收敛性。数值例子说明所给的非线性l1问题的下降算法是有效的。
本文對非線性l1問題minx∈RnF( x)=∑m i=1|fi(x)|,從理論上研究瞭F(x)的下降方嚮、最優解與某種盒式約束最小二乘問題的最優解之間的關繫,進而構造瞭一箇非線性l1問題的下降算法,併證明瞭該算法的收斂性。數值例子說明所給的非線性l1問題的下降算法是有效的。
본문대비선성l1문제minx∈RnF( x)=∑m i=1|fi(x)|,종이론상연구료F(x)적하강방향、최우해여모충합식약속최소이승문제적최우해지간적관계,진이구조료일개비선성l1문제적하강산법,병증명료해산법적수렴성。수치례자설명소급적비선성l1문제적하강산법시유효적。
This paper studied the nonlinear l1 problem:minx∈RnF( x)=∑m i=1|f i( x)|. We first discuss the descent direction of the objective function F(x) in theory,further more,we study the relation between the optimal solution of nonlinear l1 problem and the optimal solution of some kind of quadratic programming problem with box constrains. Hence, we construct a descent algorithm for nonlinear l1 problem and prove the convergence of the algorithm. An example shows that the new descent algorithm for nonlinear l1 problem is effective.