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

Abstract

An exact-penalty-function-based scheme|inspired from an old ideadue to Mayne and Polak (Math. Prog., vol. 11, 1976, pp. 67{80)|isproposed for extending to general smooth constrained optimizationproblems any given feasible interior-point method for inequality constrained problems. <p>It is shown that the primal-dual interior-point framework allows for a simpler penalty parameter update rule than that discussed and analyzed by the originators of the scheme in the context of first order methods of feasible direction. Strong global and local convergence results are proved under mild assumptions. <p>In particular,(i) the proposed algorithm does not suffer a common pitfall recently pointed out by Wachter and Biegler; and (ii) the positive definiteness assumption on the Hessian estimate, made in the original version of the algorithm, is relaxed, allowing for the use of exact Hessian information, resulting in local quadratic convergence. Promisingnumerical results are reported.<p><i>Note: This report is a major revision to <a href="http://www.isr.umd.edu/TechReports/ISR/2001/TR_2001-3/TR_2001-3.phtml">TR 2001-3,</a> "A Primal-Dual Interior-Point Method for Nonlinear Programming with Strong Global and Local Convergence Properties," by A.L. Tits, T.J. Urban, S. Bakhtiari, C.T. Lawrence.</i>