TECHNICAL NOTE: Some Structural Properties of a Newton-Type Method for Semidefinite Programs.

Using the minimum function or the Fischer­Burmeister function, we obtain two reformulations of a semidefmite 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 Fischer­Burmeister formulation. [ABSTRACT FROM AUTHOR]