A Primal-Dual Interior-Point Method for Nonlinear Programming with Strong Global and Local Convergence Properties

Abstract

A scheme---inspired from an old idea due to Mayne and Polak (Math. Prog.,vol.~11, 1976, pp.~67--80)---is proposed for extending to general smoothconstrained optimization problems a previously proposed feasibleinterior-point method for inequality constrained problems.It is shown that the primal-dual interior point framework allows for asignificantly more effective implementation of the Mayne-Polak idea thanthat discussed an analyzed by the originators in the contextof first order methods of feasible direction. Strong global and localconvergence results are proved under mild assumptions. In particular,the proposed algorithm does not suffer the Wachter-Biegler effect.