# How to minimize the trace of $G^TAG$ by using Lagrangian Multiplier method?

The problem is formulated as:

$$\max_Gtr(G^TAG)$$

where $G\in\Re^{n\times m}$, $n\geq m$, $G^TG=I$ and $A\in\Re^{n\times n}$ is positive semi-definite.

How to solve this problem by using the Lagrangian Multiplier method?

-
Minimize or maximize? –  littleO Oct 30 '12 at 8:36
That does not matter. –  mining Oct 30 '12 at 8:53