Parallel Continuous Optimization and Distributed Mathematical Collaboration

Macklem, Mason S. (2009) Parallel Continuous Optimization and Distributed Mathematical Collaboration. [Technical Report] (Unpublished)

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This report presents work on a variety of projects related to two separate areas: Part I discusses parallel direct-search optimization algorithms, and Part II involves remote mathematical collaboration. The common thread connecting the projects in these two areas is the development within the past decade of shared computing networks, such as WestGrid in Western Canada and ACEnet in Atlantic Canada, where extensive grid-computing resources are shared between multiple academic institutions. With these networks, different academic institutions are connected more quickly, creating the possibility of bringing together more researchers and allowing for easier distributed research. However, as with any increase in access to resources and information, issues arise relating to managing this increase: different projects are competing for computing resources, and a larger distributed research network can paradoxically make it more difficult to manage research relationships by increasing the pool of potential research collaborators. Part I describes a parallel implementation of a direct-search method that is designed for use on a small number of processors, for situations where limiting the number of computing resources requested will yield a higher priority placement within the job queue. We first describe an approach to load balancing by using a particular method of partitioning the set of search directions using objects from graph decomposition and graph factorization. We then present a new algorithm which uses this partitioning of the problem into independent subproblems, with local curvature information from within each subproblem used to re-align the search directions. We also consider direct-search and evolutionary strategies, comparing these two classes of methods on several standard test problems and discussing where each of these two communities can learn lessons from the other. Part II describes three projects, designed around aiding the communication of mathematical research in an increasingly distributed research community. The first involves the Federated World Directory of Mathematicians (FWDM), an online directory of mathematical researchers designed without a database in order to conform to a wide variety of international regulations regarding the collection and use of personal data. The second project discusses the process of retro-enhancement of existing mathematical literature, in which we describe the process of adding functionality to a mathematical text given a pre-existing source file, as opposed to the standard retrodigitization approach in which the source file is created from the printed document. Finally, the third project involves the C2C seminar, a cross-country seminar designed both to highlight ongoing research at one institution to the national research community, as well as to promote the computing and communication resources available on the shared computing networks involved.

Item Type: Technical Report
Additional Information: pubdom TRUE
Subjects: 68-xx Computer science
97-xx Mathematics education
49-xx Calculus of variations and optimal control; optimization
Depositing User: Mason Macklem
Date Deposited: 20 Aug 2009
Last Modified: 20 Aug 2010 14:35

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