We propose a class of preconditioners for symmetric linear systems arising from numerical analysis and nonconvex optimization frameworks. Our preconditioners are specifically suited for large indefinite linear systems and may be obtained as by-product of Krylov-subspace solvers, as well as by...

We propose a class of preconditioners, which are also tailored for symmetric linear systems from linear algebra and nonconvex optimization. Our preconditioners are specifically suited for large linear systems and may be obtained as by-product of Krylov subspace solvers. Each preconditioner in...

In this paper we consider the parameter dependent class of preconditioners M(a,d,D) defined in the companion paper The latter was constructed by using information from a Krylov subspace method, adopted to solve the large symmetric linear system Ax = b. We first estimate the condition number of...

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function consisting of a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and...