We use the proximal point method with the ϕ-divergence given by ϕ(t) = t−log t− 1 for the minimization of quasiconvex functions subject to nonnegativity constraints. We establish that the sequence generated by our algorithm is well-defined in the sense that it exists and it is not cyclical. Without any assumption of boundedness level to the objective function, we obtain that the sequence converges to a stationary point. We also prove that when the regularization parameters go to zero, the sequence converges to an optimal solution.
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