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SIAM Journal on Optimization
Article . 1991 . Peer-reviewed
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Part of book or chapter of book . 1992 . Peer-reviewed
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Article . 2020
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Direct Search Methods on Parallel Machines

Direct search methods on parallel machines
Authors: John E. Dennis Jr.; Virginia Torczon;

Direct Search Methods on Parallel Machines

Abstract

Summary: This paper describes an approach to constructing derivative-free algorithms for unconstrained optimization that are easy to implement on parallel machines. A special feature of this approach is the ease with which algorithms can be generated to take advantage of any number of processors and to adapt to any cost ratio of communication to function evaluation. Numerical tests show speed-ups on two fronts. The cost of synchronization being minimal, the speed-up is almost linear with the additional of more processors, i.e., given a problem and a search strategy, the decrease in execution time is proportional to the number of processors added. Even more encouraging, however, is that different search strategies, devised to take advantage of additional (or more powerful) processors, may actually lead to dramatic improvements in the performance of the basic algorithm. Thus search strategies intended for many processors actually may generate algorithms that are better even when implemented sequentially. The key difference is that the additional processors are not used simply to enhance the performance of an inherently sequential algorithm; they are used to spur the design of ever more ambitious --- and effective --- search strategies. The algorithms given here are supported by a strong convergence theorem, promising computational results on a variety of problems, and an intuitively appealing interpretation as multidirectional line search methods.

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Keywords

Nelder-Mead simplex algorithm, derivative-free algorithms, Numerical mathematical programming methods, Nonlinear programming, Computational methods for problems pertaining to operations research and mathematical programming, multidirectional search, unconstrained optimization, Parallel numerical computation, direct search methods

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    223
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
223
Top 1%
Top 0.1%
Top 10%
bronze