bv_cvxbook_extra_exercises

It is a variation on the problem discussed on page

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wn. However, we do have (matrix) upper 26 bounds on the covariance of the random variables yi = AT z ∈ Rki , which is AT XAi . The problem i i is to find the covariance matrix for z , that is consistent with the known upper bounds on the covariance of yi , that has the largest volume confidence ellipsoid. Derive the Lagrange dual of this problem. Be sure to state what the dual variables are (e.g., vectors, scalars, matrices), any constraints they must satisfy, and what the dual function is. If the dual function has any implicit equality constraints, make them explicit. You can assume that m T i=1 Ai Ai ≻ 0, which implies the feasible set of the original problem is bounded. What can you say about the optimal duality gap for this problem? 4.3 The relative entropy between two vectors x, y ∈ Rn is defined as ++ n xk log(xk /yk ). k=1 This is a convex function, jointly in x and y . In the following problem we calculate the vector x that minimizes the relative entropy with a given vector y , subje...
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 University of California, Berkeley.

Ask a homework question - tutors are online