PENALTY AND MULTIPLIER METHODS FOR CONSTRAINED MINIMIZATION

A generalized class of quadratic penalty function methods for the solution of nonconvex nonlinear programming problem is considered. This class contains as special cases both the usual quadratic penalty function method and the recently proposed multiplier method. Convergence and rate of convergence results are obtained for the sequences of primal and dual variables generated. The convergence results for the multiplier method are global in nature and constitute a substantial improvement over existing local convergence results. At the same time, a global duality framework is constructed for nonconvex optimization problems. The dual functional is concave, everywhere finite, and has strong differentiability properties. Furthermore, its value, gradient and Hessian matrix within an arbitrary bounded set can be obtained by unconstrained minimization of a certain augmented Lagrangian.