We consider the computation of a few eigenvectors and corresponding eigen-values of a large sparse nonsymmetric matrix. In order to compute eigenvaluesin an isolated cluster around a given shift we apply shift-and-invert Arnoldi’smethod with and without implicit restarts. For the inner iterations we useGMRES as the iterative solver. The costs of the inexact solves are measured<l...

Controllability properties of the inverse power method on projective space are investigated. For complex eigenvalue shifts a simple characterization of the reachable sets in terms of invariant subspaces can be obtained. The real case is more complicated and is investigated in this paper. Necessary and suucient conditions for complete controllability are obtained in terms of the solvability of a...

Suppose that one knows an accurate approximation to an eigenvalue of a real symmetric tridiagonal matrix. A variant of deflation by the Givens rotations is proposed in order to split off the approximated eigenvalue. Such a deflation can be used instead of inverse iteration to compute the corresponding eigenvector. © 2002 Elsevier Science Inc. All rights reserved.

In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) and Frank-Wolfe algorithm, also known as conditional gradient (CondG) method, for solving classic convex feasibility problem. Within which will be named {\it Approximate (ApDR) algorithm}, CondG method is used subroutine to compute feasible inexact projections on sets under consideration, ApDR iteration defined based ...

In this note, we consider a family of iterative formula for computing the weighted Minskowski inverses A ⊕ M,N in Minskowski space, and give two kinds of iterations and the necessary and sufficient conditions of the convergence of iterations. Keywords—iterative method, the Minskowski inverse, A ⊕ M,N inverse.

A new method is introduced for large scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the Inexact Spectral Projected Gradient method (ISPG), is implemented usi...

A novel inexact smoothing method is presented for solving the second-order cone complementarity problems (SOCCP). Our method reformulates the SOCCP as an equivalent nonlinear system of equations by introducing a regularized Chen-Harker-Kanzow-Smale smoothing function. At each iteration, Newton’s method is adopted to solve the system of equations approximately, which saves computation work compa...

We introduce Stochastic Dynamic Cutting Plane (StoDCuP), an extension of the Dual Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, builds lower bounding affine functions not only for cost-to-go functions, as SDDP does, but also some or all nonlinear cost and constraint functions. show almost sure convergence StoDCuP. inexact variant St...