A Proximal Point Algorithm with phi-Divergence to Quasiconvex Programming
F. G. M. Cunha (gevanecos.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
Entry Submitted: 07/19/2006
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