This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: UC Berkeley Department of Electrical Engineering and Computer Science EECS 227A Nonlinear and Convex Optimization Problem Set 6 Fall 2009 Issued: Thursday, November 5 Due: Thursday, November 19, 2009 Problem 6.1 B & V, Problem 5.21 Problem 6.2 B & V, Problem 5.31 Problem 6.3 B & V, Problem 5.39 Problem 6.4 B & V, Problem 5.43 Problem 6.5 Consider a problem of the form p * = min x f ( Ax + b ) + 1 2 bardbl x bardbl 2 2 where f : R m R is a convex function (whose epigraph is a closed set), and A R m n is a given matrix. The purpose of this exercise is to show that the optimal value p * is a convex function of kernel matrix K := AA T R m m . (This fact has important computational consequences for classification and regression problems.) (a) Form a dual for the problem. Hint: introduce extra variables and constraints, and use the conjugate of f in your expression of the dual. (b) Show that strong duality holds, using the result of Exercise 5.25 from BV, and prove that the function p * is convex in K ....
View
Full
Document
 Spring '11
 Staff
 Electrical Engineering

Click to edit the document details