摘要
给出了一种求解弹性l_2-l_q正则化问题的迭代重新加权l_1极小化算法,并证明了由该算法产生的迭代序列是有界且渐进正则的.对于任何有理数q∈(0,1),基于一个代数的方法,进一步证明了迭代重新加权l_1极小化算法收敛到弹性l_2-l_q(0<q<1)正则化问题的稳定点.最后,通过稀疏信号恢复的数值实例验证了算法的有效性.
In this paper, we present an iteratively re-weighted l^1 minimization （IRL1） algorithm for solving elastic l2-lq regularization. We prove that any sequence generated by the IRL1 algorithm is bounded and asymptotically regular. We further prove that the sequence is convergent based on an algebraic method for any rational q E （0, 1） and the limit is a stationary point of the elastic l2-lq （0 〈 q 〈 1） minimization problem. Numer- ical experiments on sparse signM recovery are presented to demonstrate the effectiveness of the proposed algorithm.
出处
《运筹学学报》
CSCD
北大核心
2016年第4期11-20,共10页
Operations Research Transactions
基金
国家自然科学基金(No.61071186)
