In this paper we consider the problem of efficient computation of the stochastic MV-PURE estimator which is a reduced-rank estimator designed for robust linear estimation in ill-conditioned inverse problems. Our motivation for this result stems from the fact that the reduced-rank estimation by the stochastic MV-PURE estimator, while avoiding the problem of regularization parameter selection app...

Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let F :H →H be an operator such that for some constants k,η > 0, F is k-Lipschitzian and η-strongly monotone on C; that is, F satisfies the following inequalities: ‖Fx− Fy‖ ≤ k‖x− y‖ and 〈Fx− Fy,x− y〉 ≥ η‖x− y‖2 for all x, y ∈ C, respectively. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈H . We ...

A recent letter to the editor (Quapp and Bofill, J Comput Chem 2010, 31, 2526) claims that the nudged elastic band (NEB) method can converge toward gradient extremal paths and not to steepest descent paths, as has been assumed. Here, we show that the NEB does in fact converge to steepest descent paths and that the observed tendency for the NEB to approach gradient extremal paths was a consequen...

This paper introduces the concept of a steepest ascent tariff reform for a small open economy. By construction, it is locally optimal in that it yields the highest gain in utility of any feasible tariff reform vector of the same length. Accordingly, it provides a convenient benchmark for the evaluation of the welfare effectiveness of other tariff reform proposals. We develop the properties of t...

We consider the problem of minimizing a nonlinear discrete function with L-/M-convexity proposed in the theory of discrete convex analysis. For this problem, steepest descent algorithms and steepest descent scaling algorithms are known. In this paper, we use continuous relaxation approach which minimizes the continuous variable version first in order to find a good initial solution of a steepes...

Impurity removal is a momentous part of zinc hydrometallurgy process. In this paper, hybrid modeling method mechanism and parameter estimation was proposed on the basis not changing actual production process lead-zinc smeltery. Firstly, overall nonlinear dynamic model established, then deviation between theoretical value detected outlet ion concentration taken as objective function to establish...

AdaBoost is a popular and eeective leveraging procedure for improving the hypotheses generated by weak learning algorithms. AdaBoost and many other leveraging algorithms can be viewed as performing a constrained gradient descent over a potential function. At each iteration the distribution over the sample given to the weak learner is the direction of steepest descent. We introduce a new leverag...