Most industrial processes are nonlinear systems, the control method applied consisting of a linear controller designed for the linear approximation of the nonlinear system around an operating point. However, even though the design of a linear controller is rather straightforward, the result may prove to be unsatisfactorily when applied to the nonlinear system. The natural consequence is to use ...

Although quasi-Newton algorithms generally converge in fewer iterations than conjugate gradient algorithms, they have the disadvantage of requiring substantially more storage. An algorithm will be described which uses an intermediate (and variable) amount of storage and which demonstrates convergence which is also intermediate, that is, generally better than that observed for conjugate gradient...

Quite recently Sloan and Woźniakowski [4] introduced a new notion of discrepancy, the so called weighted L discrepancy of points in the d-dimensional unit cube for a sequence γ = (γ1, γ2, . . .) of weights. In this paper we prove a nice formula for the weighted L discrepancy for even p. We use this formula to derive an upper bound for the average weighted L discrepancy. This bound enables us to...

It was shown in a previous work that some blind methods can be made robust to channel order overmodeling by using the l1 or lp quasi-norms. However, no theoretical argument has been provided to support this statement. In this work, we study the robustness of subspace blind based methods using l1 or lp quasi-norms. For the l1 norm, we provide the sufficient and necessary condition that the chann...

A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported.