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

Andre L. Tits (andreeng.umd.edu)
Andreas Waechter (andreaswwatson.ibm.co)
Sasan Bakhtiari (sasanbisr.umd.edu)
Thomas J. Urban (Thomas_Urbanjhuapl.edu)
Craig T. Lawrence (craigldc.alphatech.com)

Abstract: An exact-penalty-function-based 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 smooth constrained optimization problems any given feasible interior-point method for inequality constrained problems. 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. In particular, (i) the proposed algorithm does not suffer a common pitfall recently pointed out by Waechter 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. Promising numerical results are reported.

Keywords: primal-dual iinterior point, nonlinear programming, feasible iterates

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Technical Report TR 2002-29, Institute for Systems Research, University of Maryland, College Park, MD 20742, July 2002 To appear in SIAM J. Optimization, 2003.

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Entry Submitted: 07/19/2002
Entry Accepted: 07/21/2002
Entry Last Modified: 03/05/2003

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