Dear all
Thank you very much for your time.
Background:
I formulate the problem as:
\max_{x\in\mathcal{X}} ~\{\lambda^{T}x ~-~\max_{y\in\mathcal{Y}} x^{T}y \},
where the inside part \mathcal{F}(x):=\max_{y\in\mathcal{Y}} x^{T}y is proved to be convex in x for each y\in\mathcal{Y}. (refers to Boyd’s book, example 3.7)
Then, the total objective function is one concave function in x.
However, I failed to apply cvx to solve the cascade optimization problem, because of the inner bilinear structure, I guess.
Could anybody show me some hint to solve this problem?
Sincerely