I need to find an upper bound for the Lipschitz constant of the dual objective function. The dual objective function I have is $$max -\frac14 μ^TLL^Tμ+μ^TLy$$
L is a 999x1000 matrix
⎡1 −1 0 0 ⋯ 0 0⎤
⎢0 1 −1 0 ⋯ 0 0⎥
⎢0 0 1 −1 ⋯ 0 0⎥
⎢⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⎥
⎣0 0 0 0 ⋯ 1 −1⎦
I know I need to find an upper bound for the norm of $LL^T$
And use the following property in connection with $||Lx|| _2^2$ $\le$ $4||x|| _2^2$ $$ \lambda _{max} (A) = max(x^TAx : ||x||^2 = 1) $$ Where A is a positive semi-definite symmetric matrix and its 2-norm is given by its largest eigenvalue $\lambda _{max} (A)$
Can you please give me a step by step method from how to go from the first equation to a bound for the Lipschitz constant of the dual objective function.