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This paper addresses the worst-case evaluation complexity of a version of the standard quadratic penalty method for smooth nonconvex optimization problems with constraints. The method analysed allows inexact solution of the subproblems and do not require prior knowledge of the Lipschitz constants related with the problem. When an approximate feasible point is used as starting point, it is shown that the referred method takes at mostouter iterations to generate an  ϵ -approximate KKT point, whereis the first penalty parameter. For equality constrained problems, this bound yields to an evaluation complexity bound of, whenand suitable first-order methods are used as inner solvers. For problems having only linear equality constraints, an evaluation complexity bound ofis established when appropriate  p -order methods () are used as inner solvers. Illustrative numerical results are also presented and corroborate the theoretical predictions.

Worst-case evaluation complexity of a quadratic penalty method for nonconvex optimization