Efficiency for two problems

Hi CVX users,
I would appreciate your help on this. I have two cvx optimization problems, but one seem to be very slow and I would like to know your thoughts on it. The second problem is extremely fast but the first is extremely slow. I seem not to understand the dramatic difference in time since both terms in the norm are p by 1 vectors. I would appreciate your thoughts on it, and what I could do to make the first problem efficient.

Thanks.

p> n
U is p by n matrix
Sigmar is n by n matrix
mybeta is p by 1 vector
cvx_begin
variable alphai§
minimize(norm(alphai,1))
Utralphai=U’alphai;
subject to
norm(Sigma12
mybeta-tilderho*(USigmarUtralphai + sqrt(log§/n)*alphai),Inf)<=Tau;

cvx_end

Second problem
Sigma11 is p by p
I am able to solve Sigma11^(-1) Sigma12 very fast using SVD before inputing int CVX.
cvx_begin
variable alphai§
minimize(norm(alphai,1))
subject to
norm(Sigma11^(-1)Sigma12mybeta-tilderho
alphai),Inf)<=Tau;

cvx_end

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