I'm trying to find $$\Pi^{*} = \arg \min_{\Pi} \left[ \lambda \left( (\Pi 1 - s)^{\intercal} K (\Pi 1- s) + (\Pi^{\intercal}1-t)^{\intercal}K(\Pi^{\intercal}1-t)\right) + x^{\intercal}\Pi y \right].$$ $K$ is an $n\times n$ square matrix and $\lambda$ is a real number. Every other variable is a vector of size $n$.
My friend keeps telling me that $\Pi^{*} = 1\vec{a^{\intercal}}+\vec{b}1^{\intercal}+c\cdot yx^{\intercal}$ for some real valued vectors $\vec{a}$, $\vec{b}$, and scalar $c$. I don't see how or why this should be the case. Can anyone tell me why?