STENMIN: A software package for large, sparse unconstrained optimization using tensor methods

We describe a new package for minimizing an unconstrained nonlinear function where the Hessian is large and sparse. The software allows the user to select between a tensor method and a standard method based upon a quadratic model. The tensor method models the objective function by a fourth-order model, where the third- and fourth-order terms are chosen such that the extra cost of forming and solving the model is small. The new contribution of this package consists of the incorporation of an entirely new way of minimizing the tensor model that makes it suitable for solving large, sparse optimization problems efficiently. The test results indicate that, in general, the tensor method is significantly more efficient and more reliable than the standard Newton method for solving large, sparse unconstrained optimization problems. 12 refs., 1 tab

Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results

Tensor methods for large, sparse unconstrained optimization

Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the tensor model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method

Effect of activated alloys on hydrogen discharge kinetics of MgH2 nanocrystals

This is the post-print version of the final paper published in Journal of Alloys and Compounds. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2007 Elsevier B.V.Activated alloys synthesized by arc-melting were examined as catalysts for improving the hydrogen sorption characteristics of nanostructured magnesium hydride, proposed as a reversible hydrogen storage material. The MgH2-catalyst absorbing materials were prepared by ball milling of pure MgH2 with hydrided Zr47Ni53, Zr9Ni11, and other investigated alloys. The nanostructured MgH2-intermetallic systems were tested at 250 °C and catalyst addition of eutectoid Zr47Ni53 resulted in the fastest desorption time and highest initial desorption rate. Also, the catalyzed Mg-hydride with activated Zr9Ni11 and Zr7Ni10 phases showed fast desorption kinetics. Moreover, the results demonstrated that the composition of dispersed ZrxNiy catalysts has a strong influence on the amount of accumulated hydrogen and desorption rate of Mg-nanocomposite.National Research Council Canad

TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations

Tensor methods for large sparse systems of nonlinear equations

This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time

Cracking and Spalling Behavior of WC-17% Co Cermet Coatings

Peer reviewed: NoNRC publication: Ye