For the optimization problem, we are currently minimizing $\sum_{1\leq k\leq N} {\left(U_N^k(p)-u\right)}^2$. We might want to scale this by $\frac1N$ for consistency (e.g. for the convergence tolerance parameter).
Other forms of the criterion like $\sum \lvert U_N^k(p)-u\rvert$ or $\max U_N^k(p) - \min U_N^k(p)$ could be considered too.
For the optimization problem, we are currently minimizing $\sum_{1\leq k\leq N} {\left(U_N^k(p)-u\right)}^2$. We might want to scale this by $\frac1N$ for consistency (e.g. for the convergence tolerance parameter).
Other forms of the criterion like $\sum \lvert U_N^k(p)-u\rvert$ or $\max U_N^k(p) - \min U_N^k(p)$ could be considered too.