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A Proximal Point Algorithm with phi-Divergence to Quasiconvex Programming

F. G. M. Cunha (gevane***at***cos.ufrj.br)
J. X. da Cruz Neto (jxavier***at***ufpi.br)
P. R. Oliveira (poliveir***at***cos.ufrj.br)

Abstract: 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.

Keywords: Proximal point algorithms, phi-divergence, quasiconvex programming.

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Citation: Optimization (Journal) online 03/2010

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Entry Submitted: 07/19/2006
Entry Accepted: 07/19/2006
Entry Last Modified: 04/28/2010

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