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Unformatted text preview: University of Central Florida School of Electrical Engineering and Computer Science EGN-3420 - Engineering Analysis. Fall 2009 - dcm Project 1 due Thursday week 6 (100 points) Optimization methods Optimization problems require the determination of the extremes (maxima or minima) of continuous functions of one or more variables. One of the meth- ods to locate the value of the argument x of a function f ( x ) which maximizes or minimizes the value of the function is the golden section . If x m is an extreme of the function f ( x ) with a derivative f ( x ) then f ( x = x m ) = 0. Therefore, there should be no surprise that finding the extreme of a function f ( x ) is related to the problem of finding the roots of the equation f ( x ) = 0 for x ∈ ( x L ,s H ). The so-called bisection method for finding the roots divides the interval I = ( x L ,x H ) in half, recursively; if in this process the function g ( x ) changes signs in the interval I k = ( x L k ,x H k ) then we evaluate g ( x = x k ) with x k = ( x H k- x L k ) / 2. The new search interval becomes the subinterval where2....
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