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

Serge Gratton(serge.gratton***at***enseeiht.fr)
Vincent Malmedy(vincent.malmedy***at***fundp.ac.be)
Philppe L. Toint(philippe.toint***at***fundp.ac.be)

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 behaviour 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.

Keywords: nonlinear optimization, multilevel problems, quasi-Newton methods, nonlinear conjugate gradient methods, limited-memory algorithms

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Citation: Technical Report 09/18, Department of Mathematics, University of Namur, Namur, Belgium, November 2009

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Entry Submitted: 12/01/2009
Entry Accepted: 12/01/2009
Entry Last Modified: 12/01/2009

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