In optimization, penalty methods are used to reformulate a constraint optimization problem into several unconstrained optimization problems. It can be shown that the solutions of these derived unconstrained optimization problems will converge to the solution of the original constrained problem. For example, a minimization problem with inequality constraints can be recast as as unconstrained problems by adding a penalty term which value is a function of the original constraints. Except for minor variations penalty methods are very similar to the so-called Barrier methods.
