Abstract
Matrix augmentation is used for the inversion of bases associated with large linearly constrained control problems. It is shown how an efficient data structure can be maintained by keeping all state variables in the basis, and then nullifying some of them explicitly by using additional constraints. The proposed methodology, together with a basis updating scheme based on augmentation, forms the skeleton for an in-core algorithm using either the revised simplex method or the generalized reduced gradient method.
Similar content being viewed by others
References
J. Abadie, “Application of the GRG-algorithm to optimal control problems”, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970).
J. Bisschop and A. Meeraus, “Matrix augmentation and partitioning in the updating of the basis inverse”,Mathematical Programming 13 (1977) 241–254.
J.E. Kalan, “Aspects of large-scale in-core linear programming”,Proceedings of the 1971Annual Conference of the Association for Computing Machinery (1971).
G. Kron,Diakoptics (McDonald, London, 1956).
A.I. Propoi and V.E. Krivonozhko, “The dynamic simplex-method”, IIASA Research Memorandum RM-77-24, Laxenburg, Austria (1977).
D.J. Rose and J.R. Bunch, “The role of partitioning in the numerical solution of sparse systems”, in: D.J. Rose and R.A. Willoughby, eds.,Sparse matrices and their applications (Plenum Press, New York, 1972).
J. Sherman and W.J. Morrison, “Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix”,Annals of Mathematical Statistics 20 (1949) 621.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bisschop, J., Meeraus, A. Matrix augmentation and structure preservation in linearly constrained control problems. Mathematical Programming 18, 7–15 (1980). https://doi.org/10.1007/BF01588292
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01588292