Data assimilation covers techniques where prediction of the state of a dynamical systems is performed using data from various origins. We consider here the optimization problem that lies in the centre of this technique, when so-called variational formulations are considered. Our main interest will be focused on case where the dynamical systems under consideration is described by stochastic diff...

For large-scale sparse saddle point problems, Peng and Li [12] have recently proposed a new alternating-direction iterative method for solving nonsingular saddle point problems, which is more competitive (in terms of iteration steps and CPU time) than some classical iterative methods such as Uzawa-type and HSS (Hermitian skew splitting) methods. In this paper, we further study this method when ...

Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing...

We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special cases of these operators are used to solve some problems related to convex analysis like minimization of functionals, calculus of saddle point and variational...

A new HSS-like iterative method is first proposed based on HSS-like splitting of nonHermitian (1,1) block for solving saddle point problems. The convergence analysis for the new method is given. Meanwhile, we consider the solution of saddle point systems by preconditioned Krylov subspace method and discuss some spectral properties of the preconditioned saddle point matrices. Numerical experimen...

We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1, 1) block of the saddle point matrix. We demonstrate performance of the preconditioner on prob...

We propose a model-free shrinking-dimer saddle dynamics for finding any-index points and constructing the solution landscapes, in which force standard is replaced by surrogate model trained Gassian process learning. By this means, exact form of no longer necessary such that could be implemented based only on some observations force. This data-driven approach not avoids modeling procedure diffic...