Exact maximum-violation penalty
= Exact maximum-violation penalty
An exact maximum-violation penalty replaces inequalities $g_i(x)\leq0$ by the unconstrained objective $f(x)+M\max(0,g_1(x),\ldots,g_m(x))$. If an optimal dual multiplier is $\lambda^*$, every $M>\lVert\lambda^*\rVert_1$ makes every penalized minimizer feasible and optimal.