l_1模极小化问题的区间极大熵方法

Interval Maximum-Entropy Method for l_1 Norm Minimization Problem

利用极大熵函数思想将l1模极小化问题minx∈X(0)f(x)=|b-ATx|1(A∈Rn×m,b∈Rm,m>n≥2)近似转化为可微优化问题.在建立该问题极大熵函数及其区间扩张,证明极大熵函数及其区间扩张对原问题的收敛性质基础上,构造了l1模极小化问题的区间极大熵算法.给出了数值算例,该算法是收敛、可靠和有效的.

According to the idea of maximum-entropy function, that is, the l_1 norm minimization problem (min)x∈X^((0))f(x)=‖b-A^Tx‖_1(A∈R^(n×m),b∈R^m,m>n≥2) can be changed into a differentiable optimization problem. On the basis of discussing maximum-entropy function, interval extension. and convergence, the interval maximum-entropy method for l_1 norm minimization problem is set up. Numerical results are presented, which show that the algorithm is convergent, reliable and efficient.