bv_cvxbook_extra_exercises

# Throughout these exercises we will assume that a is

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: two meanings of the diag function: diag(w) is the diagonal matrix with the vector w on its diagonal; diag(∆X ) is the vector of the diagonal elements of ∆X .) Eliminating X from the ﬁrst equation gives an equation diag(X diag(w)X ) = 1 − diag(XCX ). This is a set of n linear equations in n variables, so it can be written as Hw = g . Give a simple expression for the coeﬃcients of the matrix H . 77 (c) Implement the feasible Newton method in Matlab. You can use X = I as starting point. The code should terminate when λ(X )2 /2 ≤ 10−6 , where λ(X ) is the Newton decrement. You can use the Cholesky factorization to evaluate the cost function: if X = LLT where L is triangular with positive diagonal then log det X = 2 i log Lii . To ensure that the iterates remain feasible, the line search has to consist of two phases. Starting at t = 1, you ﬁrst need to backtrack until X + t∆X ≻ 0. Then you continue the backtracking until the condition of suﬃcient decrease f0 (X + t∆X ) ≤ f0 (X ) +...
View Full Document

Ask a homework question - tutors are online