Finance Notes_Part_29

Finance Notes_Part_29 - does not require any smoothness...

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Extending gps to handle nonlinear constraints For unconstrained optimization, gps garantees (under a local Lipschitz assumption) to produce a limit point x such that f ( x ; d ) 0 for every d used infinitely often. Unfortunately, the d ’s are selected from a fixed finite set D , and gps may miss important directions. The effect is more pronounced as the dimension increases. Torczon and Lewis show how to adapt gps to explicit bound or linear inequalities. The directions in D are constructed using the nearby active constraints. gps is not suited for nonlinear constraints. Recently, Kolda, Lewis and Torczon proposed an augmented Lagrangean gss approach, analyzed under the assumption that the objective and constraints be twice continuously differentiable. Mads generalizes gps by allowing more directions. Mads is designed for both constrained or unconstrained optimization, and
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Unformatted text preview: does not require any smoothness assumptions. Audet and Vicente (SIOPT 2008) Optimization under general constraints 75/109 From Coordinate Search to OrthoMads OrthoMads 2008 u x k Audet and Vicente (SIOPT 2008) Optimization under general constraints 76/109 From Coordinate Search to OrthoMads OrthoMads 2008 u x k u p 1 u p 2 u p 3 u p 4 H H H H H H H H H H H H Audet and Vicente (SIOPT 2008) Optimization under general constraints 76/109 From Coordinate Search to OrthoMads OrthoMads 2008 u x k Audet and Vicente (SIOPT 2008) Optimization under general constraints 76/109 From Coordinate Search to OrthoMads OrthoMads 2008 u x k u u u u J J J J J J Audet and Vicente (SIOPT 2008) Optimization under general constraints 76/109...
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Finance Notes_Part_29 - does not require any smoothness...

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