We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f , not necessarily convex. We introduce an inexact line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the Armijo and Wolfe conditions if f is absolutely continuous along the line. Furthermore, the line search is guaranteed to terminat...

We evaluate the ability of the BATSE spectroscopy detectors to detect the absorption lines observed by Ginga in gamma ray burst spectra. We find that BATSE can detect the 20.6 keV line in the S1 segment of GB870303 with a detection probability of ∼ 1/4 in nearly normally incident bursts, with the probability dropping off to nearly 0 at a burst angle of 50◦; the lines at 19.4 and 38.8 keV lines ...

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good prop...

One of the most frequently used cues of the likelihood to purchase in a brick-and-mortar setting is the searching and browsing behavior of consumers. Retail sales employees are often trained to examine a consumer’s searching behavior in determining their likelihood to purchase. It would seem, therefore, that such a similar correlation should occur in the online setting. Namely, consumes’r searc...

Mixed-Line-Rate (MLR) optical networks provide the flexibility for satisfying heterogeneous traffic demands. However, the existence of multiple line rates makes the network planning problem more complicated. In this paper, we aim at minimizing the network cost (the joint cost of transponder, wavelength channel usage and the number of used wavelengths) for provisioning multiple multicast session...

As learning methods of a multilayer perceptron (MLP), we have the BP algorithm, Newton’s method, quasiNewton method, and so on. However, since the MLP search space is full of crevasse-like forms having a huge condition number, it is unlikely for such usual existing methods to perform efficient search in the space. This paper proposes a new search method which utilizes eigen vector descent and l...

The most important line-search algorithms for solving large-scale unconstrained optimization problems we consider in this paper are the quasi-Newton methods, truncated Newton and conjugate gradient. These methods proved to be efficient, robust and relatively inexpensive in term of computation. In this paper we compare the Dolan-Moré [11] performance profile of line-search algorithms implemented...

A two-phase descent direction method for unconstrained stochastic optimization problem is proposed. A line search method with an arbitrary descent direction is used to determine the step sizes during the initial phase, and the second phase performs the stochastic approximation (SA) step sizes. The almost sure convergence of the proposed method is established, under standard assumption for desce...

in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...