Using approximate secant equations in limited memory methods for multilevel unconstrained optimization

Authors:
Serge Gratton;Vincent Malmedy;Philippe L. Toint
Affiliations:
ENSEEIHT-IRIT, Toulouse, France 31000;Fund for Scientific Research (FNRS), Brussels, Belgium 1000 and Department of Mathematics, University of Namur (FUNDP), Namur, Belgium 5000;Namur Center for Complex Systems (NAXYS), University of Namur (FUNDP), Namur, Belgium 5000
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

The properties of multilevel optimization problems defined on a hierarchy of discretization grids can be used to define approximate secant equations, which describe the second-order behavior of the objective function. Following earlier work by Gratton and Toint (2009) we introduce a quasi-Newton method (with a linesearch) and a nonlinear conjugate gradient method that both take advantage of this new second-order information. We then present numerical experiments with these methods and formulate recommendations for their practical use.