求解一类非光滑优化问题的改进变尺度方法

1 引言 近来，人们对用过剩其函数来表示信号的处理方法表现出极大的兴趣，原因是基函数类越大所表示出的函数类就越大，人们通常采用小波基和Gabor基，本文的目的是构造一个寻找优化（或最优）基函数的算法，该算法的出发点是从过剩的其函数中选择紧支撑的基向量。

A MODIFIED AFFINE SCALING METHODOLOGY FOR NON-SMOOTH OPTIMIZATION

This paper describes a methodology to derive algorithms for non-smooth optimization. The algorithm development methodology uses slack variables and weighting coefficients for the inequality constraints and a factored representation for the gradient. The algorithm has two integral parts: a feasible initial estimate of the real signal and the iteration process that deduces the best basis selection. The iterations are based on weighted minimization of the dependent variables with the weights being sufficient small. The result of global convergence and the rate of global convergence are presented. Performance of the algorithm is illustrated on computer simulations.