Abstract
Auslender, Cominetti and Haddou have studied, in the convex case, a new family of penalty/barrier functions. In this paper, we analyze the asymptotic behavior of augmented penalty algorithms using those penalty functions under the usual second order sufficient optimality conditions, and present order of convergence results (superlinear convergence with order of convergence 4/3). Those results are related to the analysis of ‘‘pure’’ penalty algorithms, as well as ‘‘augmented’’ penalty using a quadratic penalty function. Limited numerical examples are presented to appreciate the practical impact of this local asymptotic analysis.
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