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Unformatted text preview: x f sin 2 1 ) ( 2 − = x x g x x x f x g x x x f sin 1 ) ( cos ) ( ) ( sin 2 1 ) ( 2 + = ′ − = ′ = − = 0.000000006 0.00009461 0.027103310.37758256 g(x r ) 1.673612032 1.673653810 1.685450631 1.479425538 g’(x r ) 0.739085133 0.739085134 4 0.739085134 0.739141666 3 0.739141666 0.755222417 2 0.755222417 0.5 1 x r+1 x r Comments ± Fast and simple ± may not be global ± Information about gradient is needed (differentiable) ± Can be extended to nvariable problem Update rule: where λ i is the value of λ that minimize and ( ) r i r r f x x x ∇ − = + λ 1 ( ) ( ) ( ) r r f f x x ∇ − = φ ( ) ∂ ∂ ∂ ∂ ∂ ∂ = ∇ n x f x f x f f , , , 2 1 L x Random Search ± Random generate sufficient number of candidates and find the optimal one ± Comments: ± A large number of candidates needed ± Commonly miss the best one...
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 Fall '09
 KITSANGTSANG
 Calculus, Optimization, Mathematical analysis, Global Minimum, Antenna Wireless network

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