Finance Notes_Part_5 - f x< ∞ Δ> initial mesh size...

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Coordinate search (ancestor of pattern search). Consider the unconstrained problem min x R n f ( x ) where f : R n R ∪ {∞} . Initialization : x 0 : initial point in R n such that f ( x 0 ) < Δ 0 > 0 : initial mesh size. Audet and Vicente (SIOPT 2008) Unconstrained optimization 22/109
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Coordinate search (ancestor of pattern search). Consider the unconstrained problem min x R n f ( x ) where f : R n R ∪ {∞} . Initialization : x 0 : initial point in R n such that f ( x 0 ) < Δ 0 > 0 : initial mesh size. Poll step : for k = 0 , 1 , . . . If f ( t ) < f ( x k ) for some t P k := { x k ± Δ k e i : i N } , then set x k +1 = t and Δ k +1 = Δ k ; Audet and Vicente (SIOPT 2008) Unconstrained optimization 22/109
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Coordinate search (ancestor of pattern search). Consider the unconstrained problem min x R n f ( x ) where f : R n R ∪ {∞} . Initialization : x 0 : initial point in R n such that
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Unformatted text preview: f ( x ) < ∞ Δ > : initial mesh size. Poll step : for k = 0 , 1 ,... If f ( t ) < f ( x k ) for some t ∈ P k := { x k ± Δ k e i : i ∈ N } , then set x k +1 = t and Δ k +1 = Δ k ; otherwise x k is a local minimum with respect to P k , set x k +1 = x k and Δ k +1 = Δ k 2 . Audet and Vicente (SIOPT 2008) Unconstrained optimization 22/109 Coordinate search x =(2 , 2) T , Δ =1 • f =4401 Audet and Vicente (SIOPT 2008) Unconstrained optimization 23/109 Coordinate search x =(2 , 2) T , Δ =1 • f =4401 Audet and Vicente (SIOPT 2008) Unconstrained optimization 23/109...
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