Stable exponential-penalty algorithm with superlinear convergence

A renewed interest in penalty algorithms for solving mathematical programming problems has been motivated by some recent techniques which eliminate 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 constrainst at the optimum. In this sense, interior penalty methods to be more efficient than exterior ones, but their drawback lies in the need of an interior starting point. We propose 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.