By introducing the second order Krylov subspace, a method for the reduction of second order systems is proposed leading to a reduced system of the same structure. This generalization of Krylov subspace involves two matrices and some starting vectors and the reduced order model is found by applying a projection directly to the second order model without any conversion to state space. A numerical...

Heinz von Foerster proposed that the observer should be included in the domain of observation. He suggested that this approach to cybernetics be called second-order cybernetics. Heinz was primarily interested in understanding cognition, based on neurophysiology and mathematics. But there has also been strong interest in cybernetics as a theory of social systems. Using the “second order” idea fo...

This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such considered both exact inexact forms. Using generalized differential tools variational analysis, we formulate corresponding version sufficiency use it establish, among other results, uniform growth condition...