Abstract
Consider a set of algebraic inequality constraints defining either an empty or a nonempty feasible region. It is known that each constraint can be classified as either absolutely strongly redundant, relatively strongly redundant, absolutely weakly redundant, relatively weakly redundant, or necessary. We show that is is worth making a distinction between weakly necessary constraints and strongly necessary constraints. We also present afeasible set cover method which can detect both weakly and strongly necessary constraints.
The main interest in constraint classification is due to the advantages gained by the removal of redundant constraints. Since classification errors are likely to occur, we examine how the removal of a single constraint can affect the classification of the remaining constraints.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H.C.P. Berbee, C.G.E. Boender, A.H.G. Rinnooy Kan, C.L. Scheffer, R.L. Smith and J. Telgen, “Hit-and-run algorithms for the identification of nonredundant linear inequalities,”Mathematical Programming 37 (1987) 184–207.
A. Boneh, “Identification of redundancy by a set covering equivalence,” in: J.P. Brans, ed.,Operational Research '84, Proceedings of the Tenth International Conference on Operational Research (North-Holland, Amsterdam, 1984) pp. 404–422.
A. Boneh and A. Golan, “Constraints redundancy and feasible region boundedness by a random feasible point generator (RFPG),” contributed paper,EURO III, Amsterdam, the Netherlands, April 1979.
R.J. Caron, J.F. McDonald and C.M. Ponic, “A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary,”Journal of Optimization Theory and Applications 62 (1989) 225–237.
V. Chvatal, “A greedy heuristic for the set-covering problem,”Mathematics of Operations Research 4 (1979) 233–235.
J. Gleeson and J. Ryan, “Identifying minimally infeasible subsystems of inequalities,”ORSA Journal on Computing 2 (1990) 61–64.
M.H. Karwan, V. Lotfi, J. Telgen and S. Zionts, eds.,Redundancy in Mathematical Programming (Springer, Berlin, 1983).
J. Telgen, “Redundancy and linear programs,” Ph.D. Thesis, Erasmus University (Rotterdam, The Netherlands, 1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Boneh, A., Boneh, S. & Caron, R.J. Constraint classification in mathematical programming. Mathematical Programming 61, 61–73 (1993). https://doi.org/10.1007/BF01582139
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01582139