Finance Notes_Part_21

# Finance Notes_Part_21 - Model improvement(Lagrange...

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Model improvement (Lagrange polynomials) Choose Λ > 1 . Let Y be a poised set. Each iteration of a model-improvement algorithm consists of: Estimate C = max y Y max z B |L y ( z ) | . If C > Λ then let y out correspond to the polynomial where the maximum was attained. Let y in argmax z B |L y out ( z ) | . Update Y (and the Lagrange polynomials): Y Y ∪ { y in } \ { y out } . Otherwise (i.e., C Λ ), Y is Λ –poised and stop. Audet and Vicente (SIOPT 2008) Unconstrained optimization 63/109

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Model improvement (Lagrange polynomials) Theorem For any given Λ > 1 and a closed ball B , the previous model-improvement algorithm terminates with a

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Finance Notes_Part_21 - Model improvement(Lagrange...

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