E. de Klerk

Initialization in semidefinite programming via a self-dual skew-symmetric embedding

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.

On the Convergence of the Central Path in Semidefinite Optimization

The central path in linear optimization always converges to the analytic center of the optimal set. This result was extended to semidefinite optimization in [D. Goldfarb and K. Scheinberg, SIAM J. Optim., 8 (1998), pp. 871--886]. In this paper we show that this latter result is not correct in the absence of strict complementarity. We provide a counterexample, where the central path converges to a different optimal solution. This unexpected result raises many questions. We also give a short proof that the central path always converges in semidefinite optimization by using ideas from algebraic geometry.

Improved Bounds for the Crossing Numbers of K m,n and K n

It has been long conjectured that the crossing number

Copositive realxation for genera quadratic programming

\Cr(K_{m,n})

Limiting behavior of the central path in semidefinite optimization

of the complete bipartite graph

A note on the stability number of an orthogonality graph

K_{m,n}

Parallel implementation of a semidefinite programming solver based on CSDP on a distributed memory cluster

equals the Zarankiewicz number

On Semidefinite Programming Relaxations of (2+ p )-SAT

Z(m,n):= \floor{\frac{m-1}{2}} \floor{\frac{m}{2}} \floor{\frac{n-1}{2}} \floor{\frac{n}{2}}

POLYNOMIAL PRIMAL-DUAL AFFINE SCALING ALGORITHMS IN SEMIDEFINITE PROGRAMMING

. Another longstanding conjecture states that the crossing number

On the Complexity of Optimization Over the Standard Simplex

\Cr(K_n)