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 x ≥ 0, based on the iterative scheme: x ∈ argmin{f(x)+ μkd(x, x k−1)}, where d(·, ·) is an entropy-like distance function. The algorithm is welldefined 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 μk approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained.