Selective Gram–Schmidt orthonormalization for conic cutting surface algorithms

John Mitchell () and Vasile Basescu ()

Mathematical Methods of Operations Research, 2008, vol. 67, issue 1, 115 pages

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. Copyright Springer-Verlag 2008

Keywords: Semidefinite programming; Conic programming; Column generation; Cutting plane methods (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s00186-007-0177-6

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