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Unformatted text preview: Let { Y k } be the sequence of simplices generated. Let f be bounded from below and uniformly continuous in R n . Theorem (Step size going to zero) The diameters of the simplices converge to zero: lim k→ + ∞ diam ( Y k ) = 0 . Theorem (Global convergence) If f is continuously diﬀerentiable in R n and { Y k } lies in a compact set then { Y k } has at least one stationary limit point x * . Audet and Vicente (SIOPT 2008) Unconstrained optimization 45/109 Simplex gradients It is possible to build a simplex gradient: y y 1 y 2 ∇ s f ( y ) = ± y 1y y 2y ²> ³ f ( y 1 )f ( y ) f ( y 2 )f ( y ) ´ . Audet and Vicente (SIOPT 2008) Unconstrained optimization 46/109...
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 Spring '06
 Tapley
 Finance, Calculus, Topology, Metric space, Compact space, Unconstrained Optimization

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