# Can CVX solve convex non differentiable optimization problem?

I want to solve minimization of maximum eigen value of symmetric matrix, this is non-differentiable convex problem.
I am not getting global optimum. Can anyone explain the reason.

minimize lambda_max(Ginv(G1)) ( wrt matrix U)
subject to G=G1+U
all G, G1 and U are 2
2 matrices.

thanks

What is your actual CVX model? In particular, what is “Ginv(G1)”? That doesn’t look symmetric, which `lambda_max` requires; and if it is not symmetric, it is probably not convex.

What is your actual CVX model? In particular, what is “Ginv(G1)”? That doesn’t look symmetric, which `lambda_max` requires; and if it is not symmetric, it is probably not convex.

function is lambda ( G* Inverse(G1)) … it can be converted into lyapounov form : Transpose(G)PG1 + Transpose(G1)PG … this is LMI and hence convex, but eigen value function is usually non -differentiable.

It is still not clear to me what your model is. But if you can express it using LMIs, then yes, CVX can solve it. In its original form, no it cannot.