Classic and Logarithmic-Quadratic Proximal Point Method for Quasiconvex Minimization

Erik Papa Quiroz (erikcos.ufrj.br)
Paulo Roberto Oliveira (poliveircos.ufrj.br)

Abstract: This paper extends the full convergence of the classic and logarithmic-quadratic proximal point method to solve continuous quasiconvex minimization problems in Euclidean spaces and in the positive orthant. Under the assumption that the global minimizer set is nonempty we prove the full convergence of the sequence generated by the method to a certain generalized critical point of the problem, and convergence to a KKT point for the logarithmic-quadratic method when the objective function is continuously differentiable..

Keywords: Proximal point algorithm, Quasiconvex functions, Limiting subdifferential, Frechet Subdifferential

Category 1: Nonlinear Optimization (Unconstrained Optimization )

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

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Entry Submitted: 06/21/2006
Entry Accepted: 06/21/2006
Entry Last Modified: 11/22/2006

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