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Finance Notes_Part_12

# Finance Notes_Part_12 - Generalized pattern search f =2341...

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Generalized pattern search x 1 =(1 , 2) T , Δ 1 =2 f =101 f =150 f =2341 f =967 Audet and Vicente (SIOPT 2008) Unconstrained optimization 31/109

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Generalized pattern search x 2 =(2 , 2) T , Δ 2 =1 f =101 Audet and Vicente (SIOPT 2008) Unconstrained optimization 32/109
Generalized pattern search x 2 =(2 , 2) T , Δ 2 =1 f =101 A search trial point. Ex: built using a simplex gradient Audet and Vicente (SIOPT 2008) Unconstrained optimization 32/109

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Convergence analysis If all iterates belong to a bounded set, then lim inf k Δ k = 0 . Corollary There is a convergent subsequence of iterates x k ˆ x of mesh local optimizers, on meshes that get infinitely fine. Audet and Vicente (SIOPT 2008) Unconstrained optimization 33/109
Convergence analysis If all iterates belong to a bounded set, then
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