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Finance Notes_Part_33

# Finance Notes_Part_33 - Filter approach to...

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Unformatted text preview: Filter approach to constraints (Based on Fletcher - Leyffer) min x ∈ Ω f ( x ) The extreme barrier handles the closed and hidden constraints X . A filter handles C ( x ) ≤ . Define the nonnegative constraint violation function h ( x ) := X j max(0 ,c j ( x )) 2 if x ∈ X and f ( x ) < ∞ , ⇐ open constraints + ∞ otherwise. ⇐ closed constraints h ( x ) = 0 if and only if x ∈ Ω . The constrained optimization problem is then viewed as a biobjective one: to minimize f and h , with a priority to h . This allows trial points that violate the open constraints. Audet and Vicente (SIOPT 2008) Optimization under general constraints 82/109 Filter approach to constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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Finance Notes_Part_33 - Filter approach to...

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