Technical Note: Some Structural Properties of a Newton-Type Method for Semidefinite Programs

C. Kanzow and C. Nagel
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C. Kanzow: University of Würzburg
C. Nagel: University of Würzburg

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 1, No 10, 219-226

Abstract: Abstract Using the minimum function or the Fischer-Burmeister function, we obtain two reformulations of a semidefinite program as a nonlinear system of equations. Applying a Newton-type method to such a reformulation leads to a linear system of equations which has to be solved at each iteration. We discuss some properties of this linear system and show that the corresponding coefficient matrix is symmetric positive definite for the minimum function approach and positive definite but unsymmetric for the Fischer-Burmeister formulation.

Keywords: Semidefinite programs; Newton's method; Smoothing methods (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTA.0000041737.19689.4c

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