bv_cvxbook_extra_exercises

# Suppose f rn r is a posynomial function x y rn 1 and

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: r ℓp -norms with rational p. (a) Use the observation at the beginning of exercise 4.26 in Convex Optimization to express the constraint √ y, z1 , z2 ≥ 0, y ≤ z1 z2 , with variables y , z1 , z2 , as a second-order cone constraint. Then extend your result to the constraint y ≤ (z1 z2 · · · zn )1/n , y ≥ 0, z 0, where n is a positive integer, and the variables are y ∈ R and z ∈ Rn . First assume that n is a power of two, and then generalize your formulation to arbitrary positive integers. (b) Express the constraint f (x) ≤ t as a second-order cone constraint, for the following two convex functions f : xα x ≥ 0 0 x < 0, f (x) = where α is rational and greater than or equal to one, and f (x) = xα , dom f = R++ , where α is rational and negative. (c) Formulate the norm approximation problem minimize 22 Ax − b p as a second-order cone program, where p is a rational number greater than or equal to one. The variable in the optimization problem is x ∈ Rn . The matrix A ∈ Rm×n and the vector b ∈ Rm are...
View Full Document

## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

Ask a homework question - tutors are online