A Proximal Point Algorithm with phi-Divergence to Quasiconvex Programming

We use the proximal point method with the phi-divergence given by phi(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.


Optimization (Journal) online 03/2010