Finance Notes_Part_10

# Finance Notes_Part_10 - For k = 0 , 1 ,... Search step :...

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Generalized pattern search – Torczon 1996 Initialization : x 0 : initial point in R n such that f ( x 0 ) < Δ 0 > 0 : initial mesh size. D : ﬁnite positive spanning set of directions. Audet and Vicente (SIOPT 2008) Unconstrained optimization 29/109

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Generalized pattern search – Torczon 1996 Initialization : x 0 : initial point in R n such that f ( x 0 ) < Δ 0 > 0 : initial mesh size. D : ﬁnite positive spanning set of directions. Deﬁnition D = { d 1 ,d 2 ,...,d p } is a positive spanning set if ± p X i =1 α i d i : α i 0 ,i = 1 , 2 ,...p ² = R n . Remark : p n + 1 . Deﬁnition (Davis) D = { d 1 ,d 2 ,...,d p } is a positive basis is it is a positive spanning set and no proper subset of D is a positive spanning set. Remark : n + 1 p 2 n . Audet and Vicente (SIOPT 2008) Unconstrained optimization 29/109
Generalized pattern search – Torczon 1996 Initialization : x 0 : initial point in R n such that f ( x 0 ) < Δ 0 > 0 : initial mesh size. D : ﬁnite positive spanning set of directions.

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Unformatted text preview: For k = 0 , 1 ,... Search step : Evaluate f at a ﬁnite number of mesh points. Poll step : If the search failed, evaluate f at the poll points { x k + Δ k d : d ∈ D k } where D k ⊂ D is a positive spanning set. Parameter update : Set Δ k +1 < Δ k if no new incumbent was found, otherwise set Δ k +1 ≥ Δ k , and call x k +1 the new incumbent. Audet and Vicente (SIOPT 2008) Unconstrained optimization 29/109 Generalized pattern search x =(2 , 2) T , Δ =1 • f =4401 Audet and Vicente (SIOPT 2008) Unconstrained optimization 30/109 Generalized pattern search x =(2 , 2) T , Δ =1 • f =4401 Audet and Vicente (SIOPT 2008) Unconstrained optimization 30/109...
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## This document was uploaded on 10/30/2011 for the course FIN 3403 at University of Florida.

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Finance Notes_Part_10 - For k = 0 , 1 ,... Search step :...

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