CAJ | 학술논문

本文给出了提出了求解绝对值方程组稀疏解的两种算法：其一是l 1方法。利用‖x‖1来逼近‖x‖0，文中证明了该方法实质上是求解一个线性规划问题；其二是重新加权的l 1方法。利用一个凹函数来逼近‖x‖0，并且对该凹函数进行线性化近似，通过求解一系列的线性规划问题来找到绝对值方程组的稀疏解。文中给出了两种方法的联系。数值试验的结果表明：两种算法均是求解绝对值方程组稀疏解的非常有效的算法。
본문급출료제출료구해절대치방정조희소해적량충산법：기일시l 1방법。이용‖x‖1래핍근‖x‖0，문중증명료해방법실질상시구해일개선성규화문제；기이시중신가권적l 1방법。이용일개요함수래핍근‖x‖0，병차대해요함수진행선성화근사，통과구해일계렬적선성규화문제래조도절대치방정조적희소해。문중급출료량충방법적련계。수치시험적결과표명：량충산법균시구해절대치방정조희소해적비상유효적산법。
In this paper, two methods for solving sparse solution of absolute value equations are proposed. One of these methods is l1 method in which ‖x‖1 is used to approximate ‖x‖ 0 . It is proved that in fact l1 problem is a linear programming. The other method is a reweighed l1 method in which a concave function is used to approximate‖x‖0 . By using linearization technique to the concave function, an algorithm for finding sparse solution of absolute value equations is proposed. The main part of this algorithm is solving a series of linear programming. The collections between the two methods are given. The results of the numerical experiments about these two methods are given which show that the two methods are all very efficiently in finding sparse solution of absolute value equations.