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# HW9 - ELE 704 Optimization HW9 Due 15 May 2007 1 Newtons...

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ELE 704 Optimization HW9 Due 15 May, 2007 1. Newton’s method with fixed step size α = 1 can diverge if the initial point is not close to x * . Consider the following examples: (a) f ( x ) = log( e x + e - x ) has a unique minimizer at x * = 0. i. Plot f ( x ) for x [ - 2 , 2] (You may want to draw in the logarith- mic scale.) ii. Run Newton’s method by hand with fixed step size α = 1, start- ing at x (0) = 1 and at x (0) = 1 . 1 iii. Plot the trajectory of x ( k ) on the figure of part ( a.i ) for the first 5 iterations and also draw f ( x ( k ) ) - p * vs. number of iterations. (b) Repeat part (a) for f ( x ) = - log( x ) + x which has the unique mini- mizer at x * = 1. Start at x (0) = 3 . (c) Comment on your results. 2. Write the MATLAB code for pure Newton Method and run for the func- tions of Q.1 starting at the given initial points. Verify your answer with
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