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.
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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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Mitchell, J.E., Basescu, V.L. Selective Gram–Schmidt orthonormalization for conic cutting surface algorithms. Math Meth Oper Res 67, 91–115 (2008). https://doi.org/10.1007/s00186-007-0177-6
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DOI: https://doi.org/10.1007/s00186-007-0177-6