This is a convex problem and how it can be solved by Lagrange duality method, although it can be well solved by CVX. The derivations with regard to Lk and Bk are constants, which means the closed-form solution cannot be presented. I feel confused and I really want to see some insights that help me understand the problem deeply. I will give my honest appreciation to these who clear up the doubts for me.
As you said, you can solve it using CVX. if you want help to solve it in some other way, I suggest posting on another forum, such as https://or.stackexchange.com/ .
Thanks. I’ll seek help to that forum.