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Unformatted text preview: UC Berkeley Department of Electrical Engineering and Computer Science EECS 227A Nonlinear and Convex Optimization Problem Set 4 Fall 2009 Issued: Tuesday, October 6 Due: Thursday, October 15, 2009 Reading: Boyd and Vandenberghe: Chapter 2, 4.3, 4.4 Problem 4.1 (d) This set is convex because it can be expressed as \ y S { x k x x k 2 k x y k 2 } , i.e., an intersection of halfspaces. (Note that k x x k 2 k x y k 2 x T x 2 x T x + x T x x T x 2 x T y + y T y 2( y x ) T x + x T x y T y so the set y S { x k x x k 2 k x y k 2 } is a halfspace) (e) In general this set is not convex, for example with S = { 1 , 1 } and T = { } , we have { x  dist ( x,S ) dist ( x,T ) } = { x R  x  1 / 2 or x 1 / 2 } which clearly is not convex. (g) This set is convex, in fact a ball { x k x a k 2 k x b k 2 } = { x k x a k 2 2 k x b k 2 2 } = { x  (1 2 ) x T x 2( a 2 b ) T x + ( a T a 2 b T b ) } If = 1, this is a halfspace. If= 1, this is a halfspace....
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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 University of California, Berkeley.
 Spring '11
 Staff
 Electrical Engineering

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