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An Overview on Projection-Type Methods for Convex Large-Scale Quadratic Programs

  • Chapter
Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 58))

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Abstract

A well-known approach for solving large and sparse linearly constrained quadratic programming (QP) problems is given by the splitting and projection methods. After a survey on these classical methods, we show that they can be unified in a general iterative scheme consisting in to solve a sequence of QP subproblems with the constraints of the original problem and an easily solvable Hessian matrix. A convergence theorem is given for this general scheme. In order to improve the numerical performance of these methods, we introduce two variants of a projection- type scheme that use a variable projection parameter at each step. The two variable projection methods differ in the strategy used to assure a sufficient decrease of the objective function at each iteration. We prove, under very general hypotheses, the convergence of these schemes and we propose two practical, nonexpensive and efficient updating rules for the projection parameter. An extensive numerical experimentation shows the effectiveness of the variable projection-type methods.

This work was supported by MURST Project “Numerical Analysis: Methods and Mathematical Software” and by CNR Research Contribution N. 98.01029.CT01, Italy.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Ferrara, Via Machiavelli, 35, 44100, Ferrara, Italy

    Valeria Ruggiero

  2. Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi, 213/b, 41100, Modena, Italy

    Luca Zanni

Authors
  1. Valeria Ruggiero
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  2. Luca Zanni
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Editor information

Editors and Affiliations

  1. University of Pisa, Italy

    Franco Giannessi

  2. University of Catania, Italy

    Antonino Maugeri

  3. University of Florida, USA

    Panos M. Pardalos

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© 2001 Kluwer Academic Publishers

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Ruggiero, V., Zanni, L. (2001). An Overview on Projection-Type Methods for Convex Large-Scale Quadratic Programs. In: Giannessi, F., Maugeri, A., Pardalos, P.M. (eds) Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Nonconvex Optimization and Its Applications, vol 58. Springer, Boston, MA. https://doi.org/10.1007/0-306-48026-3_18

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  • DOI: https://doi.org/10.1007/0-306-48026-3_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-0161-1

  • Online ISBN: 978-0-306-48026-3

  • eBook Packages: Springer Book Archive

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