A proximal-like algorithm for a class of nonconvex programming
Jein-Shan Chen, Shaohua Pan · Pacific Journal of Optimization · 2008
In this paper, we study a proximal-like algorithm for minimizing a closed proper function f(x) subject to x ‚ 0, based on the iterative scheme: x 2 argminff(x)+ kd(x;x ki1 )g, where d(¢;¢) is an entropy-like distance function. The algorithm is well- deflned under the assumption that the problem has a nonempty and bounded solution set. If, in addition, f is a difierentiable quasi-convex function (or f is a difierentiable function which is homogeneous with respect to a solution), we show that the sequence generated by the algorithm is convergent (or bounded), and furthermore, it converges to a solution of the problem (or every accumulation point is a solution of the problem) when the parameter k approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained.