On the decrease of a quadratic function along the projected-gradient path.
Minimization of a convex quadratic function subject to separable conical constraints in granular dynamics
The numerical solution of granular dynamics problems with Coulomb friction leads to the problem of minimizing a convex quadratic function with semidefinite Hessian subject to a separable conical constraints. In this paper, we are interested in the numerical solution of this problem. We suggest a modification of an active-set optimal quadratic programming algorithm. The number of projection steps is decreased by using a projected Barzilai-Borwein method. In the numerical experiment, we compare our...
Rozděl a slep aneb jak řešit soustavu s bilionem lineárních rovnic
Cílem článku je naznačit úlohu matematiky a efektivnost nových algoritmů pro řešení rozsáhlých soustav lineárních rovnic na současných masívně paralelních superpočítačích. Na příkladu řešení Poissonovy rovnice je popsána základní varianta metody rozložení oblasti typu FETI (finite element tearing and interconnecting) s projektorem na přirozenou hrubou síť, jsou odvozeny základní kvalitativní výsledky demonstrující asymptoticky lineární (optimální) složitost řešení a jsou popsána prakticky důležitá...
Uniqueness of the operator attaining
-norm of iterates and the spectral radius of matrices
Inexact solution of auxiliary problems in Polyak type algorithms
Rennie's generalization of Kantorovich's inequality in a Hilbert space
Polynomials of the eigenvalues and powers of matrices
A note on estimate of the spectral radius of symmetric matrices
Negative powers and the spectrum of matrices
The critical exponent of operators with constrained spectral radius
On the penalty approximation of quadratic programming problem
Scalable algorithms for contact problems with geometrical and material non-linearities
Solution of muscle-bone contact problem in biomechanics
On conditioning of Schur complements of H-TFETI clusters for 2D problems governed by Laplacian
Bounds on the spectrum of the Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients in the analysis of many domain decomposition methods. Here we are interested in the analysis of floating clusters, i.e. subdomains without prescribed Dirichlet conditions that are decomposed into still smaller subdomains glued on primal level in some nodes and/or by some averages. We give the estimates of the regular condition number of the Schur complements...
Nonmonotone strategy for minimization of quadratics with simple constraints
An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified...
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