Let $F: \mathbb{R}^N\to\mathbb{R}$ be a strictly convex function, and let $x^*=argmin_x F(x)$. Further, let $A:\mathbb{R}^N\to\mathbb{R}^k$ be some fixed matrix, where $k<<N$.
I want to compute $y=Ax^*$ .
Is there any kind of trick to compute this that is easier than directly computing $x^*$? Some kind of keyword for this that appears in the convex optimization literature? Any pointers are appreciated.