 On strata of degenerate polyhedral cones I: Condition and distance to strataDennis Cheung, Felipe Cucker and Javier Pea European Journal of Operational Research, 2009, vol. 198, issue 1, 23-28 Abstract: Systems Ay[greater-or-equal, slanted]0 with a degenerate cone of solutions are considered ill-posed since finite-precision algorithms are not expected to find points in the cone of solutions. Consequently, common condition numbers for these systems, such as C(A) [J. Renegar. Some perturbation theory for linear programming, Mathematical Programming 65 (1994) 73-91] and [D. Cheung, F. Cucker, A new condition number for linear programming, Mathematical Programming 91 (2001) 163-174], which are based on the notion of distance to the nearest ill-posed problem, become infinite on such ill-posed instances. In this paper, we extend these two condition numbers to versions and which are always finite. Both condition numbers can be expressed in terms of a distance to a change in the geometry of the cone of solutions. The main result shows that for both of them, the distance corresponds to a notion of best conditioned solution for a canonical complementarity problem associated to the system Ay[greater-or-equal, slanted]0. Keywords: Polyhedral; conic; systems; Degeneracy; Condition; numbers (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:198:y:2009:i:1:p:23-28 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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