In this paper we derive a decay rate of the L-norm of the solution to the 2-D dissipative quasi-geostrophic flows comparing with the corresponding linear equation. We use a new, concise and direct method to avoid using the Fourier splitting technique completely and make the paper be self-contained without using any previous decay result. Mathematics Subject Classification(2000): 35Q35, 76D05

The notion of quasi-Fejér monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. Applications to convex optimization and inverse problems are demon...

A new approach to the problem of minimizing L2sensitivity subject to L2-norm scaling constraints for state-space digital filters is proposed. Using linearalgebraic techniques, the problem at hand is converted into an unconstrained optimization problem, and the unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. Computer simulation results are presented...

A nonmonotone strategy for solving nonlinear systems of equations is introduced. The idea consists of combining eecient local methods with an algorithm that reduces monotonically the squared norm of the system in a proper way. The local methods used are Newton's method and two quasi-Newton algorithms. Global iterations are based on recently introduced box-constrained minimization algorithms. We...

The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subse...

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions, like the Euclidean norm, that are nonsmooth at the minimizer.

In this paper, we provide a H 1 {norm lower bound on the worst{case identiication error of least{squares estimation when using FIR model structures. This bound increases as a logarithmic function of model complexity and is valid for a wide class of inputs characterized as being quasi{stationary with covariance function falling oo suuciently quickly.

This paper reports theoretical and empirical investigations on the use of quasi-Newton methods to minimize the Optimal Bellman Residual (OBR) of zero-sum two-player Markov Games. First, it reveals that state-of-the-art algorithms can be derived by the direct application of Newton’s method to different norms of the OBR. More precisely, when applied to the norm of the OBR, Newton’s method results...

The theory of compressed sensing has shown that sparse signals can be reconstructed exactly from remarkably few measurements by solving a nonconvex underdetermined lp-regularized quasi-norm problem via an iterative weighted least-squares problem. In this work, we consider the problem of recovering an input signal by solving a nonconvex overdetermined lp-regularized quasi-norm problem. In order ...