Copyright © [2003] by The Society for Industrial and Applied Mathematics. All rights reserved
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.
By: Andre L. Tits, Andreas Waechter, Sasan Bakhtiari, Thomas J. Urban, Craig T. Lawrence
Published in: SIAM Journal on Optimization, volume 14, (no 1), pages 173-99 in 2003
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