Let $M_{n}$ denote the set of $n\times n$ real matrices. Let $c>0$ be a real number and denote by $X_1,X_2,...,X_n$ the lines of the matrix $X\in M_n$. Let $\|X_i\|$ denote the euclidian norm of $X_i$.
Let $M_n^c=\{X\in M_n:\ \|X_i\|\leq c\ \forall\ i\in\{1,...,n\}\}$ and $\operatorname{det}:M_n\rightarrow \mathbb{R}$ be the determinant function.
The problem is: maximize the function $\operatorname{det}$ over $M_n^c$.