In this paper we discuss inexact Uzawa algorithms and inexact nonlinear Uzawa algorithms to solve discretized variational inequalities of the second kind. We prove convergence results for the algorithms. Numerical examples are included to show the effectiveness of the algorithms.

This paper presents a practical guide for use of the ScalIT software package to perform highly accurate bound rovibrational spectroscopy calculations for triatomic molecules. At its core, ScalIT serves as a massively scalable iterative sparse matrix solver, while assisting modules serve to create rovibrational Hamiltonian matrices, and analyze computed energy levels (eigenvalues) and wavefuncti...

In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a Quasi-Newton method combined with a p block iterative row-projection linear solver of Cimmino-type, 1 p n: Under weak regularity conditions for F; it is proved that this Inexact Quasi-Newton method has a local, linear convergence in the energy norm induced by the precondit...

This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis, Schenk, and Wächter [SIAM J. Sci. Comput., 32 (2010), pp. 3447-3475], a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in ...

Nonlinear elliptic transport systems arise in various problems in applied mathematics, most often leading to large-scale problems owing to the huge number of equations, see e.g. [14, 17, 18]. For large-scale elliptic problems, iterative processes are the most widespread solution methods, which often rely on Hilbert space theory when mesh independence is desired. (See e.g. [7, 11, 12] and the au...

In view of the minimization of a nonsmooth nonconvex function f , we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the KurdykaLojasiewicz inequality. This assumption allows to cover a wide ...

In many applications in finance, insurance, and reinsurance, one seeks a solution of finding a covariance matrix satisfying a large number of given linear equality and inequality constraints in a way that it deviates the least from a given symmetric matrix. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper,...

We are concerned with structural optimization problems in CFD where the state variables are supposed to satisfy a linear or nonlinear Stokes system and the design variables are subject to bilateral pointwise constraints. Within a primaldual setting, we suggest an all-at-once approach based on interior-point methods. The discretization is taken care of by Taylor-Hood elements with respect to a s...

In this paper we present the results obtained in the solution of sparse and large systems of non-linear equations by inexact Newton methods combined with an block iterative row-projection linear solver of Cimmino-type. Moreover, we propose a suitable partitioning of the Jacobian matrix A. In view of the sparsity, we obtain a mutually orthogonal row-partition of A that allows a simple solution o...

A major computational issue in the finite element (FE) integration of coupled consolidation equations is the repeated solution in time of the resulting discretized indefinite system. Because of ill-conditioning, the iterative solution, which is recommended in large size 3D settings, requires the computation of a suitable preconditioner to guarantee convergence. In this paper the coupled system ...