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On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

Marco D'Apuzzo(marco.dapuzzo***at***unina2.it)
Valentina De Simone(valentina.desimone***at***unina2.it)
Daniela di Serafino(daniela.diserafino***at***unina2.it)

Abstract: The solution of KKT systems is ubiquitous in optimization methods and often dominates the computation time, especially when large-scale problems are considered. Thus, the effective implementation of such methods is highly dependent on the availability of effective linear algebra algorithms and software, that are able, in turn, to take into account specific needs of optimization. In this paper we discuss the mutual impact of linear algebra and optimization, focusing on interior point methods and on the iterative solution of the KKT system. Three critical issues are addressed: preconditioning, termination control for the inner iterations, and inertia control.

Keywords: large-scale optimization, interior point methods, KKT system, constraint preconditioners, adaptive stopping criteria, inertia control.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Preprint n.1-08, Department of Mathematics, Second University of Naples, March, 2008

Download: [PDF]

Entry Submitted: 03/12/2008
Entry Accepted: 03/12/2008
Entry Last Modified: 03/12/2008

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