lecture13

# lecture13 - Lecture Applying Golden Section Search Method...

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Lecture 2/19/08 Applying Golden Section Search Method Using Spreadsheets Introduction to Linear Programming

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Review of Golden Section Search Can be used to solve the following NLP Maximize f(x) Such that a ≤ x ≤ b 6180 . 2 5 1 - r = ± = Assume: I k = interval of uncertainty after k iterations = [a k ,b k ] Golden Ratio:
Outline of Algorithm Evaluate f(x) at two points x 2k-1 and x 2k on the interval [a k ,b k ] x 2k-1 =b k -r(b k -a k ) x 2k =a k +r(b k -a k ) I k+1 =[a k+1 , b k+1 ] = Interval of uncertainty for k+1 st iteration If f(x 2k-1 ) < f(x 2k ) a k+1 =x 2k-1 and b k+1 = b k If f(x 2k-1 ) ≥ f(x 2k ) a k+1 =a k and b k+1 =x 2k

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Applications of Mathematical Optimization Determining Product Mix Manufacturing Routing and Logistics Financial Planning Diet Problem
General Form of an Optimization Problem MAX (or MIN): f (X 1 ,X 2 ,…, X n ) Subject to: f 1 (X 1 , X 2 , …, X n ) b 1 f k (X 1 , X 2 , …, X n ) b k : f m (X 1 , X 2 , …, X n )=b m

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lecture13 - Lecture Applying Golden Section Search Method...

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