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An inexact and nonmonotone proximal method for smooth unconstrained minimization

S. A. Santos (sandra***at***ime.unicamp.br)
R. C. M. Silva (rmesquita***at***ufam.edu.br)

Abstract: An implementable proximal point algorithm is established for the smooth nonconvex unconstrained minimization problem. At each iteration, the algorithm minimizes approximately a general quadratic by a truncated strategy with step length control. The main contributions are: (i) a framework for updating the proximal parameter; (ii) inexact criteria for approximately solving the subproblems; (iii) a nonmonotone criterion for accepting the iterate. The global convergence analysis is presented, together with numerical results that validate and put into perspective the proposed approach.

Keywords: Proximal point algorithms; regularization; nonconvex problems; unconstrained minimization; global convergence; nonmonotone line search; numerical experiments.

Category 1: Nonlinear Optimization (Unconstrained Optimization )


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Entry Submitted: 05/24/2013
Entry Accepted: 05/24/2013
Entry Last Modified: 11/11/2013

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