Proximal Linear Methods for DC Composite Minimization Problems

In this paper, we introduce two linearized proximal algorithms for solving DC composite optimization problems. The basic algorithms we rely are the proximal-linear(ized) methods, which in each iteration solve regularized subproblems formed by linearizing the smooth map and the concave component, respectively. It is proved that the two proposed algorithms provide descent methods and that if the sequences generated by the algorithms are bounded, every cluster points are critical points of the functions under consideration. Finally, a conclusion is stated and some directions for further research are suggested