I’m computer science student. Iam looking for some helps concerning the resolution of an optimization problem.
I have an optimization problem defined on two sets \mathcal{X}=\{x_i\}_{i=1}^n and \mathcal{Y}=\{y_j\}_{j=1}^m and described as follows

I think what you have to do here is assemble the matrices X and Y from those inner products, so that X_{ij}=x_i^Tx_j and Y_{ij}=y_{ij}, etc. Once you do that, I think the objective becomes