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Description: |
Pattern search methods can be made more efficient if past function
evaluations are appropriately reused. This class of methods is widely used
in practice due to its simplicity and easy implementation, but the
corresponding algorithms have the major drawback of sometimes using many
expensive function values. Although efficiency can be improved by using surrogates in the
search step, the sampling process inherent to the polling step is partially
responsible for the number of function values required. In this talk we will introduce a
number of ways of reusing previous evaluations of the objective function to
improve the efficiency of a pattern search iteration.
For instance, at each iteration of a pattern search method, one can attempt
to compute an accurate simplex gradient by identifying a sampling set of
previous iterates with good geometrical properties. This simplex gradient
can then be used to reorder the evaluations of the objective function
associated with the positive spanning set or positive basis used in the
poll step. But it can also be used to update the mesh size parameter
according to a sufficient decrease criterion. None of these modifications
demands new function evaluations. Surrogate-models based on simplex
derivatives can also be considered in the search step.
We will present these procedures in detail and apply them to a set of
problems which includes test problems from the CUTEr collection and two
applications problems (one related to the simulation of a mechanical system
with contact and another resulting from parameter estimation in
astrophysics). The numerical results show that these procedures can enhance
significantly the practical performance of pattern search methods.
This is joint work with Luís Nunes Vicente (Departamento de Matemática
da FCTUC e Centro de Matemática da Universidade de Coimbra).
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Date: |
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| Start Time: |
14.30 |
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Speaker: |
Ana Luísa Custódio (FCT, UNL, CMUC)
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Place: |
Room 5.5
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| Research Groups: |
-Numerical Analysis and Optimization
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See more:
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