Abstract: "In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so- called bordered block diagonal form. More precisely, given some matrix A, we try to assign as many rows as possible to some number [beta] of blocks of size [ka...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Borndörfer, Ralf 1967- (VerfasserIn), Ferreira, Carlos E. (VerfasserIn), Martin, Alexander 1965- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin Konrad-Zuse-Zentrum für Informationstechnik 1997
Schriftenreihe:	Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin 1997,15
Schlagworte:	Decomposition (Mathematics) Integer programming Matrices
Zusammenfassung:	Abstract: "In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so- called bordered block diagonal form. More precisely, given some matrix A, we try to assign as many rows as possible to some number [beta] of blocks of size [kappa] such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the LP- and MIP- libraries Netlib and Miplib can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs."
Beschreibung:	26 S.