A Newton Acceleration of the Weiszfeld Algorithm forMinimizing the Sum of Euclidean Distances
Computational Optimization and Applications
Condition numbers for polyhedra with real number data
Operations Research Letters
On the condition numbers for polyhedra in Karmarkar's form
Operations Research Letters
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
Hi-index | 0.00 |
An equilibrium system (also known as a Karush--Kuhn--Tucker (KKT) system, a saddlepoint system, or a sparse tableau) is a square linear system with a certain structure. Strang [SIAM Rev., 30 (1988), pp.~283--297] has observed that equilibrium systems arise in optimization, finite elements, structural analysis, and electrical networks. Recently, Stewart [Linear Algebra Appl., 112 (1989), pp.~189--193] established a norm bound for a type of equilibrium system in the case when the "stiffness" portion of the system is very ill-conditioned. This paper investigates the algorithmic implications of Stewart's result. It is shown that several algorithms for equilibrium systems appearing in applications textbooks are unstable. A certain hybrid method is then proposed, and it is proved that the new method has the right stability property.