In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the step size sequence {ηt}t for the convergence of an OMD algorithm with respect to the expected Bregman distance induced by the mirror map. The condition is limt→...

In this paper, we evaluate the performance of a new class of conjugate gradient methods for training recurrent neural networks which ensure the sufficient descent property. The presented methods preserve the advantages of classical conjugate gradient methods and simultaneously avoid the usually inefficient restarts. Simulation results are also presented using three different recurrent neural ne...

In this paper, a new conjugate conjugate method with sufficient descent property is proposed for the unconstrained optimization problem. An attractive property of the new method is that the descent direction generated by the method always possess the sufficient descent property, and this property is independent of the line search used and the choice of ki  . Under mild conditions, the global c...

A closed subspace M in a Banach space X is called t/-proximinal if it satisfies: (1 + p)S n (S + M) ç S + e(pXS n M), for some positive valued function t(p), p > 0, and e(p) -» 0 as p -> 0, where 5 is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are (/-proximinal, for ...

Additively separable functions on RN are of the form I;= 1 Ui(Xi). These functions have the obvious property that they are completely separable. That is, the induced orders on the (N 1)-dimensional sets {(x,, . . . , xN): xi0 = c} are independent of c. A natural question is whether the opposite is also true, that is, whether complete separability of a function V implies additive separability. D...

Conjugate gradient methods (CG) constitute excellent neural network training that are simplicity, flexibility, numerical efficiency, and low memory requirements. In this paper, we introduce a new three-term conjugate method, for solving optimization problems it has been tested on artificial networks (ANN) feed-forward network. The method satisfied the descent condition sufficient condition. Glo...

The notion of key privacy for encryption schemes was defined formally by Bellare, Boldyreva, Desai and Pointcheval in Asiacrypt 2001. This notion seems useful in settings where anonymity is important. In this short note we describe a (very simple) sufficient condition for key privacy. In a nutshell, a scheme that provides data privacy is guaranteed to provide also key privacy if the distributio...

The interaction of two isotropic turbulent fields of equal integral scale but different kinetic energy generates the simplest kind of inhomogeneous turbulent field. In this paper we present a numerical experiment where two time decaying isotropic fields of kinetic energies E1 and E2 initially match over a narrow region. Within this region the kinetic energy varies as a hyperbolic tangent. The f...

In an important step forward Maskin (1977) showed that two properties −Monotonicity and No Veto Power − form a sufficient condition for Nash implementation when conjoinet. In contrast to the vast literature that followed, this characterization has two big advantages: First, it is often easy to verify, and second, it has an elegant and simple interpretation. However, there does not exist a simil...