A proximal-like algorithm for a class of nonconvex programming

In this paper, we study a proximal-like algorithm for minimizing a closed proper function f(x) subject to x³0, based on the iterative scheme: x^k ε argmin{f(x) + μkd(x, x^k-1)}, where d( , ) is an entropy-like distance function. The algorithm is well-defined under the assumption that the problem has a nonempty and bounded solution set. If, in addition, f is a differentiable quasi-convex function (or f is a differentiable 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 μ^k approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained.