Strong Duality Thresholds and Minimum Curvature for the Nearest Rectangular Symplectic Matrix Problem

We study the nearest rectangular symplectic matrix problem in the squared Frobenius norm for arbitrary targets $T\in\mathbb R^{2n\times2k}$, with $n\ge k$. We prove that its semidefinite relaxation is exact for every target if and only if $n\ge2k-1$. Under this condition, the primal problem, the rel