Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Symmetric indefinite systems for interior point methods
Mathematical Programming: Series A and B
Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
Large-scale semidefinite programs in electronic structure calculation
Mathematical Programming: Series A and B
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This paper deals with a semidefinite program (SDP) having free variables, which often appears in practice. To apply the primal---dual interior-point method, we usually need to convert our SDP into the standard form having no free variables. One simple way of conversion is to represent each free variable as a difference of two nonnegative variables. But this conversion not only expands the size of the SDP to be solved but also yields some numerical difficulties which are caused by the non-existence of a primal---dual pair of interior-feasible solutions in the resulting standard form SDP and its dual. This paper proposes a new conversion method that eliminates all free variables. The resulting standard form SDP is smaller in its size, and it can be more stably solved in general because the SDP and its dual have interior-feasible solutions whenever the original primal---dual pair of SDPs have interior-feasible solutions. Effectiveness of the new conversion method applied to SDPs having free variables is reported in comparison to some other existing methods.