For positive semi-definite matrices $A,B$, how can I find an $X$ that minimizes $\text{Trace}(AX^TBX$) under the constraint:that $X$ is orthogonal.All the matrices have real entries and $A,B$ are square while $X$ is rectangular. Thanks.This is what I have:Define $B=F^{T}F$. Define $Y=FX$. You get the above problem as \begin{align}\min_{Y}~ \text{trace}(AY^{T}Y)\end{align}But now I want $X^*$ that minimizes the original problem. This is what is confusing me! 
Trace minimization with an orthogonality constraint
ds.algorithms;optimization;linear algebra