Stability of saddle point problems with penalty

An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term

Stability estimates and structural spectral properties of saddle point problems

For a general class of saddle point problems sharp estimates for Babuška’s inf-sup stability constants are derived in terms of the constants in Brezzi’s theory. In the finite-dimensional Hermitian case more detailed spectral properties of preconditioned saddle point matrices are presented, which are helpful for the convergence analysis of common Krylov subspace methods. The theoretical results ...

Maxima to Saddle-point Problems

Saddle-Point Dynamics: Conditions for Asymptotic Stability of Saddle Points

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradientascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is a...

Preconditioners for Generalized Saddle-point Problems Preconditioners for Generalized Saddle-point Problems *

We examine block-diagonal preconditioners and efficient variants of indefinite preconditioners for block two-by-two generalized saddle-point problems. We consider the general, nonsymmetric, nonsingular case. In particular, the (1,2) block need not equal the transposed (2,1) block. Our preconditioners arise from computationally efficient splittings of the (1,1) block. We provide analyses for the...