Finance Notes_Part_2

Finance Notes_Part_2 - (gradient) . Audet and Vicente...

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Limitations of derivative-free optimization iteration k x k - x * k 0 1.8284e+000 1 5.9099e-001 2 1.0976e-001 3 5.4283e-003 4 1.4654e-005 5 1.0737e-010 6 1.1102e-016 Newton methods converge quadratically (locally) but require first and second order derivatives (gradient and Hessian) . Audet and Vicente (SIOPT 2008) Introduction 8/109
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Limitations of derivative-free optimization iteration k x k - x * k 0 3.0000e+000 1 2.0002e+000 2 6.4656e-001 . . . . . . 6 1.4633e-001 7 4.0389e-002 8 6.7861e-003 9 6.5550e-004 10 1.4943e-005 11 8.3747e-008 12 8.8528e-010 Quasi Newton (secant) methods converge superlinearly (locally) but require first order derivatives
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Unformatted text preview: (gradient) . Audet and Vicente (SIOPT 2008) Introduction 9/109 Limitations of derivative-free optimization In DFO convergence/stopping is typically slow (per function evaluation): Audet and Vicente (SIOPT 2008) Introduction 10/109 Pitfalls The objective function might not be continuous or even well dened: Audet and Vicente (SIOPT 2008) Introduction 11/109 Pitfalls The objective function might not be continuous or even well dened: Audet and Vicente (SIOPT 2008) Introduction 12/109...
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Finance Notes_Part_2 - (gradient) . Audet and Vicente...

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