- Convergence Analysis of an Interior-Point Method for Nonconvex Nonlinear Programming Hande Y. Benson(bensondrexel.edu) Arun Sen(senpost.harvard.edu) David F. Shanno(shannonew-rutcor.rutgers.edu) Abstract: In this paper, we present global and local convergence results for an interior-point method for nonlinear programming. The algorithm uses an $\ell_1$ penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’s strictly feasible interior-point method [6]. The global convergence of the algorithm is proved under mild assumptions, and local analysis shows that it converges Q-quadratically. The proposed approach improves on existing results in several ways: (1) the convergence analysis does not assume boundedness of dual iterates, (2) local convergence does not require the Linear Independence Constraint Qualification, (3) the solution of the penalty problem is shown to locally converge to optima that may not satisfy the Karush-Kuhn-Tucker conditions, and (4) the algorithm is applicable to mathematical programs with equilibrium constraints. Keywords: interior-point methods, penalty methods, convergence Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF]Entry Submitted: 06/13/2007Entry Accepted: 06/13/2007Entry Last Modified: 06/13/2007Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.