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Unformatted text preview: meshes that get inﬁnitely ﬁne. If f is Lipschitz near ˆ x , then f ◦ (ˆ x,v ) ≥ for all v ∈ T H Ω (ˆ x ) . Assuming more smoothness, Abramson studies second order convergence. Audet and Vicente (SIOPT 2008) Optimization under general constraints 79/109 Open, closed and hidden constraints Consider the toy problem: min x ∈ R 2 x 2 1√ x 2 s.t.x 2 1 + x 2 2 ≤ 1 x 2 ≥ Audet and Vicente (SIOPT 2008) Optimization under general constraints 80/109 Open, closed and hidden constraints Consider the toy problem: min x ∈ R 2 x 2 1√ x 2 s.t.x 2 1 + x 2 2 ≤ 1 x 2 ≥ Closed constraints must be satisﬁed at every trial vector of decision variables in order for the functions to evaluate. Here x 2 ≥ is a closed constraint, because if it is violated, the objective function will fail. Audet and Vicente (SIOPT 2008) Optimization under general constraints 80/109...
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This document was uploaded on 10/30/2011 for the course FIN 3403 at University of Florida.
 Spring '06
 Tapley
 Finance

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