| 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: xk ∈ argmin{ f(x )+ μkd (x, xk-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 μk approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained. |
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