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Vladimir Yu. Protasov (Moscow State University)
| Speaker: |
Vladimir Yu. Protasov
(Moscow State University, Russia)
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| Date: |
Friday July 3, 2009
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| Title: |
Derivative-free
minimization of convex functions
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Abstract
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Is it
possible to compute effectively the minimal value of a multivariate
function without computing its derivative? The
general answer is ``No´´, unless the function
is convex. For convex functions one can find the minimum with any
relative precision involving only values of the functions. Such
algorithms exist and quite efficient (at least, theoretically) even for
very large number of variables. They use a well-known idea of the
cutting-plane algorithm, or the method of central cross-sections.
We discuss the developing of this method, its relation to other
well-known algorithms (ellipsoid method, etc.) We are also going
to see why is that difficult to put the algorithms of derivative-free
minimization to practice, despite their theoretical efficiency.
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