Equivalence of Two Nondegeneracy Conditions for Semidefinite Programs

M. L. Flegel and C. Kanzow ()
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M. L. Flegel: University of Würzburg
C. Kanzow: University of Würzburg

Journal of Optimization Theory and Applications, 2007, vol. 135, issue 3, No 6, 397 pages

Abstract: Abstract Nondegeneracy assumptions are often needed in order to prove the local fast convergence of suitable algorithms as well as in the sensitivity analysis for semidefinite programs. One of the more standard nondegeneracy conditions is the geometric condition used by Alizadeh et al. (Math. Program. 77:111–128, 1997). On the other hand, Kanzow and Nagel (SIAM J. Optim. 15:654–672, 2005) recently introduced an algebraic condition that was used in order to prove, for the first time, the local quadratic convergence of a suitable algorithm for the solution of semidefinite programs without using the strict complementarity assumption. The aim of this paper is to show that these two nondegeneracy conditions are equivalent.

Keywords: Semidefinite programs; Nondegeneracy conditions; Strict complementarity (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-007-9270-5

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