Validation of an Augmented Lagrangian Algorithm with a Gauss-Newton Hessian Approximation Using a Set of Hard-Spheres Problems

Authors:
Nataša Krejić;José Mario Martínez;Margarida Mello;Elvio A. Pilotta
Affiliations:
Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia. natasa@unsim.im.ns.ac.yu;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil. martinez@ime.unicamp.br;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil. margarid@ime.unicamp.br;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil. pilotta@ime.unicamp.br
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

An Augmented Lagrangian algorithm that uses Gauss-Newton approximations of the Hessian at each inner iteration is introduced and tested using a family of Hard-Spheres problems. The Gauss-Newton model convexifies the quadratic approximations of the Augmented Lagrangian function thus increasing the efficiency of the iterative quadratic solver. The resulting method is considerably more efficient than the corresponding algorithm that uses true Hessians. A comparative study using the well-known package LANCELOT is presented.