Abstract
This paper examines the question of modifying the decomposition of a partially separable function in order to improve computational efficiency of large-scale minimization algorithms using a conjugate-gradient inner iteration. The context and motivation are given and the application of a simple strategy discussed on examples extracted from the CUTE test problem collection.
This research was supported in part by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No F49620-91-C-0079. The United States Government is authorized to reproduce and distribute reprints for governmental purpose notwithstanding any copyright notation hereon.
The authors wish to acknowledge additional funding provided by a NATO travel grant.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bertsekas, D. P. (1982), Constrained Optimization and Lagrange Multipliers Methods. Academic Press, London.
Bongartz, I., Conn, A. R., Gould, N. and Toint, Ph. L. (1993), CUTE: Constrained and Unconstrained Testing Environment, Technical Report 93/10, Department of Mathematics, FUNDP, Namur, Belgium.
Chang, S. F. and McCormick, S. T. (1992), “A hierarchical algorithm for making sparse matrices sparser,” Mathematical Programming 56 (1), 1–31.
Conn, A. R, Gould, N. and Toint, Ph. L. (1990), “An introduction to the structure of large scale nonlinear optimization problems and the LANCELOT project,” In R. Glowinski and A. Lichnewsky, editors, Computing Methods in Applied Sciences and Engineering, pages 42–51, Philadelphia, USA. SIAM.
Conn, A. R., Gould, N. and Toint, Ph. L. (1991), “A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds,” SIAM Journal on Numerical Analysis 28(2), 545–572.
Conn, A. R., Gould, N. and Toint, Ph. L. (1992), A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds, Technical Report 92/07, Department of Mathematics, FUNDP, Namur, Belgium.
Conn, A. R., Gould, N. and Toint, Ph. L. (1992), LANCELOT; a Fortran package for large-scale nonlinear optimization (Release A). Number 17 in Springer Series in Computational Mathematics. Springer Verlag, Heidelberg, Berlin, New York.
Griewank, A. and Toint, Ph. L. (1982), “On the unconstained optimization of partially separable functions,” In M. J. D. Powell, editor, Nonlinear Optimization 1981, pages 301–312, London and New York. Academic Press.
Griewank, A. and Toint, Ph. L. (1982), “Partitioned variable metric updates for large structured optimization problems,” Numerische Mathematik 39, 119–137.
Nemhauser, G. L. and Wolsey, L. A. (1988), Integer and Combinatorial Optimization. J. Wiley and Sons, New York.
Powell, M. J. D. (1969), “A method for nonlinear constraints in minimization problems,” In R. Fletcher, editor, Optimization, London and New York. Academic Press.
Toint, Ph. L. (1987), “On large scale nonlinear least squares calculations,” SIAM Journal on Scientific and Statistical Computing 8(3), 416–435.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Kluwer Academic Publishers
About this chapter
Cite this chapter
Conn, A.R., Gould, N., Toint, P.L. (1994). Improving the Decomposition of Partially Separable Functions in the Context of Large-Scale Optimization: a First Approach. In: Hager, W.W., Hearn, D.W., Pardalos, P.M. (eds) Large Scale Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3632-7_5
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3632-7_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3634-1
Online ISBN: 978-1-4613-3632-7
eBook Packages: Springer Book Archive