hw3_fa09_rev

hw3_fa09_rev - UC Berkeley Department of Electrical...

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Unformatted text preview: UC Berkeley Department of Electrical Engineering and Computer Science EECS 227A Nonlinear and Convex Optimization Problem Set 3 Fall 2009 Issued: Tuesday, September 22 Due: Tuesday, October 6, 2009 Problem 3.1 Consider applying Newtons method to the cost function bardbl x bardbl , where > 1. (a) Suppose that we use the pure form of Newtons method (i.e., stepsize k = 1). For what starting points and values of does the method converge to the optimal solution? What happens when 1? (b) Repeat part (a) for Newtons method using Armijo rule to choose step sizes. Problem 3.2 Let Q R n n be a strictly positive definite symmetric matrix. (a) Show that bardbl x bardbl Q = radicalbig x T Qx defines a valid norm on R n . (b) State and prove a generalization of the projection theorem from class that involves bardbl z x bardbl Q . (c) Let H k R n n be a positive definite matrix, and let C be a convex set. For a current iterate x k and parameter s k > 0, define...
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hw3_fa09_rev - UC Berkeley Department of Electrical...

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