bv_cvxbook_extra_exercises

# 98 093 y 2 101 101 1 00 0 0 1 0 p2

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: ickest slab separating two sets. We are given two sets in Rn : a polyhedron C1 = {x | Cx d}, deﬁned by a matrix C ∈ Rm×n and a vector d ∈ Rm , and an ellipsoid C2 = {P u + q | u 2 ≤ 1}, deﬁned by a matrix P ∈ Rn×n and a vector q ∈ Rn . We assume that the sets are nonempty and that they do not intersect. We are interested in the optimization problem maximize inf x∈C1 aT x − supx∈C2 aT x subject to a 2 = 1. with variable a ∈ Rn . Explain how you would solve this problem. You can answer the question by reducing the problem to a standard problem class (LP, QP, SOCP, SDP, . . . ), or by describing an algorithm to solve it. Remark. The geometrical interpretation is as follows. If we choose 1 b = ( inf aT x + sup aT x), 2 x ∈C 1 x ∈C 2 then the hyperplane H = {x | aT x = b} is the maximum margin separating hyperplane separating C1 and C2 . Alternatively, a gives us the thickest slab that separates the two sets. 7.8 Bounding object position from multiple camera views. A...
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