On solving three classes of nonlinear programming problems via simple differentiable penalty functions

We consider the following classes of nonlinear programming problems: the minimization of smooth functions subject to general constraints and simple bounds on the variables; the nonlinearl ₁-problem; and the minimax problem. Numerically reliable methods for solving problems in each of these classes, based upon exploiting the structure of the problem in constructing simple differentiable penalty functions, are presented.This research was made possible by NSERC Grant No. A8442.The author would like to thank Mrs. J. Selwood of the Department of Combinatories and Optimization, University of Waterloo, Ontario, Canada for her excellent typesetting.This work was carried out in the Department of Combinatories and Optimization, University of Waterloo, Waterloo, Ontario, Canada.