 Power penalty

For an equality-constrained optimization problem, an even integer $p\ge 2$ makes this a nonnegative penalty for constraint violation. Its derivative is $\nabla f+{\mu }^{-1}D{c}^T{c}^{p-1}$, with the power applied coordinatewise. The case $p=2$ is the quadratic penalty. Reducing $\mu$ increases the cost of infeasibility; it does not itself ensure that computed stationary points or minimizers stay bounded.