Finance Notes_Part_23

Finance Notes_Part_23 - Mads and the extreme barrier for...

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Minimum Frobenius norm models Motivation comes from : The models are built by minimizing the entries of the Hessian ( in the Frobenius norm ) subject to the interpolation conditions. In this case, one can prove that H is bounded: k H k C ( n ) C ( f ) C ( Y ) . Or they can be built by minimizing the difference between the current and previous Hessians ( in the Frobenius norm ) subject to the interpolation conditions. In this case, one can show that if f is itself a quadratic then: k H - ∇ 2 f k ≤ k H old - ∇ 2 f k . Audet and Vicente (SIOPT 2008) Unconstrained optimization 68/109
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Presentation outline 1 Introduction 2 Unconstrained optimization 3 Optimization under general constraints Nonsmooth optimality conditions
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Unformatted text preview: Mads and the extreme barrier for closed constraints Filters and progressive barrier for open constraints 4 Surrogates, global DFO, software, and references Limitations of gps Optimization applied to the meeting logo. Level sets of f : R 2 R : f ( x ) = 1-e-k x k 2 max {k x-c k 2 , k x-d k 2 } Audet and Vicente (SIOPT 2008) Optimization under general constraints 70/109 Limitations of gps u Audet and Vicente (SIOPT 2008) Optimization under general constraints 70/109 Limitations of gps u c c c c Audet and Vicente (SIOPT 2008) Optimization under general constraints 70/109...
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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_23 - Mads and the extreme barrier for...

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