Unconstrained optimization algorithms

(Problem) is the problem of estimating the matrix norm for a (possibly rectangular) matrix , using its definition as an (unconstrained) maximum problem.

(Alg1) is a standard gradient descent (steepest descent) approach.

(Alg2) is a a quasi-Newton method such as BFGS (one which does not require any approximations of the Hessian of the function)