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A penalty method incorporates constraint violation into the objective with a parameter controlling its cost. For an equality constraint $c(x)=0$, the quadratic penalty method adds a multiple of $\Vert c(x){\Vert }_2^2$; a power penalty uses higher even powers. The penalty can allow infeasible iterates while encouraging feasibility as the cost grows. This differs from a logarithmic barrier, whose domain itself excludes the constraint boundary and exterior. Existence of a penalized stationary point, convergence of its constraint violation and convergence of the primal points are separate questions.