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 Newton’s method to the cost function bardbl x bardbl β , where β > 1. (a) Suppose that we use the pure form of Newton’s method (i.e., stepsize α k = 1). For what starting points and values of β does the method converge to the optimal solution? What happens when β ≤ 1? (b) Repeat part (a) for Newton’s 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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## This note was uploaded on 09/03/2011 for the course EE 227A taught by Professor Staff during the Spring '11 term at Berkeley.

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hw3_fa09_rev - UC Berkeley Department of Electrical...

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