Convergence behavior of interior-point algorithms
Mathematical Programming: Series A and B
An OnL -iteration homogeneous and self-dual linear programming algorithm
Mathematics of Operations Research
SIAM Review
On homogeneous and self-dual algorithms for LCP
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
An Exact Duality Theory for Semidefinite Programming and its Complexity Implications
An Exact Duality Theory for Semidefinite Programming and its Complexity Implications
On Semidefinite Programming Relaxations of (2+p)-SAT
Annals of Mathematics and Artificial Intelligence
A New Self-Dual Embedding Method for Convex Programming
Journal of Global Optimization
Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
Optimization Methods & Software
The minimum-rank gram matrix completion via modified fixed point continuation method
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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The formulation of interior point algorithms for semidefinite programming has become an active research area, following the success of the methods for large-scale linear programming. Many interior point methods for linear programming have now been extended to the more general semidefinite case, but the initialization problem remained unsolved. In this paper we show that the initialization strategy of embedding the problem in a self-dual skew-symmetric problem can also be extended to the semidefinite case. This method also provides a solution for the initialization of quadratic programs and it is applicable to more general convex problems with conic formulation.