DIFFERENTIABLE EXACT PENALTY FUNCTIONS FOR NONLINEAR SECOND-ORDER CONE PROGRAMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We propose a method for solving nonlinear second-order cone programs (SOCPs), based on a continuously differentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method has global and superlinear convergence. We also present some preliminary numerical experiments.22416071633Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Japan Society for the Promotion of ScienceFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2010/20572-0, 2011/23638-5]CNPq [PRONEX-CNPq/FAPERJ E-26/171.510/2006-APQ1]CNPq [305740/2010-5