We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspacemethods.We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditi...

In this paper, we propose and investigate a new homogenization method for diffusion problems in domains with multiple inclusions with big values of diffusion coefficients. The diffusion problem is approximated by the P1-finite element method on a triangular mesh. The underlying algebraic problem is replaced by a special system with a saddle point matrix. For the solution of the saddle point sys...

In this paper two preconditioners for the saddle point problem are analysed: one based on the augmented Lagrangian approach and another involving artificial compressibility. Eigenvalue analysis shows that with these preconditioners small condition numbers can be achieved for the preconditioned saddle point matrix. The preconditioners are compared with commonly used preconditioners from literatu...

Kramers’ exit problem is concerned with noise activated escape from a potential well. In case the noise strength, , (temperature measured in units of potential barrier height) is small this becomes a singular perturbation problem. It is shown that actually, most of the probability of the exit points on the separatrix is located at a distance O( √ ) from the saddle point and the probability vani...

The Karush–Kuhn–Tucker (KKT) optimality conditions and saddle point optimality conditions in fuzzy programming problems have been studied in literature by various authors under different conditions. In this paper, by considering a partial order relation on the set of fuzzy numbers, and convexity with differentiability of fuzzy mappings, we have obtained the Fritz John (FJ) constraint qualificat...

We extend recent work on the connection between loopy belief propagation and the Bethe free energy. Constrained minimization of the Bethe free energy can be turned into an unconstrained saddle-point problem. Both converging double-loop algorithms and standard loopy belief propagation can be interpreted as attempts to solve this saddle-point problem. Stability analysis then leads us to conclude ...

A p-norm surrogate constraint method is proposed in this paper for integer programming. A single surrogate constraint can be always constructed using p-norm such that the feasible sets in a surrogate relaxation and the primal problem match exactly. The p-norm surro-gate constraint method is thus guaranteed to succeed in identifying the optimal solution of the primal problem with zero duality ga...

We deal with the iterative solution of linear systems arising from so-called dual-dual mixed finite element formulations. The linear systems are of a two-fold saddle point structure; they are indefinite and ill-conditioned. We define a special inner product that makes matrices of the two-fold saddle point structure, after a specific transformation, symmetric and positive definite. Therefore, th...