STABLE EXPONENTIAL-PENALTY ALGORITHM WITH SUPERLINEAR CONVERGENCE

A renewed interest in penalty algorithms for solving mathematical prog ramming problems has been motivated by some recent techniques which el iminate the ill-conditioning caused by the convergence to zero of the penalty parameter. These techniques are based on a good identification of the active set of constraints at the optimum. In this sense, inter ior penalty methods seem to be more efficient than exterior ones, but their drawback lies in the need of an interior starting point. We prop ose in this paper an exponential penalty function which does not need interior starting points, but whose ultimate behavior is just like an interior penalty method. A superlinearly convergent algorithm based on the exponential penalty function is proposed.