A general result is obtained for the existence of saddle-point in a stochastic game of timing, by exploiting its connection with a bounded-variation control problem. Weak compactness arguments prove the existence of an optimal process for the control problem. It is shown that this optimal process generates a pair of stopping times that constitute a saddle-point for the game, using the method of...

Two new methods for solving the symmetric saddle point problem are proposed. The first one is a generalization of Golub’s method for the augmented system formulation (ASF) and uses the Householder QR decomposition. The second method is supported by the singular value decomposition (SVD). Numerical comparison of some direct methods are given.

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for the ability of these local methods to find the global minimum is the proliferation o...

Abstract BDDCalgorithms have previously been extended to the saddle point problems arising frommixed formulations of elliptic and incompressible Stokes problems. In these two-level BDDC algorithms, all iterates are required to be in a benign space, a subspace in which the preconditioned operators are positive definite. This requirement can lead to large coarse problems, which have to be generat...

In this report we study the stability of a nonsymmetric saddle-point problem. It is discretized with equal order finite elements and stabilized with a consistent regularization. In this way we achieve a stable finite element discretization of optimal order approximation properties.

The Signorini problem describes the contact of a linearly elastic body with a rigid frictionless foundation. It is transformed into a saddle point problem of some augmented Lagrangian functional and then discretized by nite element methods. Optimal error estimates are obtained for general smooth domains which are not necessarily convex. The key ingredient in the analysis is a discrete inf-sup c...

Abstract We investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting multiple species. An approach inspired by augmented Lagrangian methods allows us to construct symmetric positive definite Onsager matrix, in turn leads an effective numerical algorithm. prove inf-sup conditions f...

We consider saddle-point problems that typically arise from the mixed finite element discretization of second order elliptic problems. By proper equivalent algebraic operations the considered saddle-point problem is transformed to another saddle-point problem. The resulting problem can then be efficiently preconditioned by a block-diagonal matrix or by a factored block-matrix (the blocks corres...

The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equa...