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Differentiable exact penalty functions for nonlinear second-order cone programs

Ellen H. Fukuda (ellen***at***ime.usp.br)
Paulo J. S. Silva (pjssilva***at***ime.usp.br)
Masao Fukushima (fuku***at***i.kyoto-u.ac.jp)

Abstract: We propose a method to solve 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.

Keywords: Nonlinear second-order cone program, exact penalty functions, semismooth reformulation, generalized Newton method.

Category 1: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 2: Nonlinear Optimization

Citation: SIAM Journal on Optimization 22(4), 1607–1633, 2012.

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Entry Submitted: 10/19/2011
Entry Accepted: 10/19/2011
Entry Last Modified: 01/24/2013

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