CG Global Convergence Properties with Goldstein Linesearch*

This paper explores the convergence of nonlinear conjugate gradient methods with Goldstein line search without regular restarts. Under this line search, global convergence for a subsequence is given for the famous conjugate gradient methods, Fletcher-Reeves method. The same result can be obtained for Polak-Ribiére-Polyak method and others. *This work was partially supported by National Hitech Program (863,2002AA104540) and National Natural Science Foundation of China (No.60373060).     

A Goldstein's Type Projection Method for a Class of Variant Variational Inequalities

Some optimization problems in mathematical programming can be translated to a variant variational inequality of the following form: Find a vector $\u^*$,such that $$Q(u^*)∈Ω,(v-Q(u^*))^Tu^* ≥ 0, ∀_v∈Ω.$$. This paper presents a simple iterative method for solving this class of variational inequalities. The method can be viewed as an extension of the Goldstein's projection method. Some results of preliminary numerical experiments are given to indicate its applications.     

Well Hydraulics with the Weber–Goldstein Transforms

Two new integral transforms, ideally suited for solving boundary value problems in well hydraulics, are derived from one of the Goldstein identities which generalizes a corresponding Weber identity. The two transforms are, therefore, named the Weber–Goldstein transforms. Their properties are presented. For the first, second, and third type boundary conditions, the new transforms remove the radial portion of a Laplacian in the cylindrical coordinates. They are used to straightforwardly rederive known solutions to the problems of a fully penetrating flowing well and a fully penetrating pumped well. A novel solution for a fully penetrating flowing well with infinitesimal skin situated in a leaky aquifer is also found by means of one of the new transforms. This solution is validated by comparison to a numerical solution obtained via the finite-difference method and to a quasi-analytic solution obtained by numerical inversion of the corresponding solution in the Laplace domain. Based on the new solution, a flowing well test is proposed for estimating the hydraulic conductivity and specific storativity of the aquifer and the skin factor of the well. The test can also be used in a constant-head injection mode. A type-curve estimation procedure is developed and illustrated with an example. The effectiveness of the test in estimating the well skin factor and aquifer parameters depends on the availability of data on the sufficiently early well response.     

Secondary molecular mobility in amorphous ethyl cellulose: Aging effects and degree of co‐operativity

The secondary relaxations in amorphous ethyl cellulose are studied using thermally stimulated depolarization currents (TSDCs) in the temperature region from 165 °C (108 K) up to 145 °C (418 K). The influence of aging on the current peaks of the secondary relaxation is discussed, and it is concluded that some modes of motion of this mobility are aging independent, while others are affected by aging. A particular attention is focused on the discussion of the degree of co‐operativity of the motional modes of the secondary relaxation. The conclusion to be driven from the obtained TSDC results is that the aging‐independent motional modes, as well as those that are aging dependent, do not show any appreciable co‐operative character. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 820–829, 2009     

Identities for the Hankel transform and their applications

In the present paper the authors show that iterations of the Hankel transform with Kν-transform is a constant multiple of the Widder transform. Using these iteration identities, several Parseval-Goldstein type theorems for these transforms are given. By making use of these results a number of new Goldstein type exchange identities are obtained for these and the Laplace transform. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.     

在Goldstein搜索下一类共轭梯度法的全局收敛性

本文证明了文「１」提出的一类共轭梯度法在Ｇｏｌｄｓｔｅｉｎ非精确线性搜索下具有全局收敛性。