Selective Gram–Schmidt orthonormalization for conic cutting surface algorithms |
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Authors: | John E Mitchell Vasile L Basescu |
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Institution: | (1) Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA;(2) Baltimore, MD, USA |
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Abstract: | It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization
problem. Examples of conic constraints include semidefinite constraints and second order cone constraints. In this paper,
a method to slightly modify the constraints is proposed. Because of this modification, a simple procedure to generate strictly
feasible points in both the primal and dual spaces can be defined. A second benefit of the modification is an improvement
in the complexity analysis of conic cutting surface algorithms. Complexity results for conic cutting surface algorithms proved
to date have depended on a condition number of the added constraints. The proposed modification of the constraints leads to
a stronger result, with the convergence of the resulting algorithm not dependent on the condition number.
Research supported in part by NSF grant number DMS-0317323. Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. |
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Keywords: | Semidefinite programming Conic programming Column generation Cutting plane methods |
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