Nocedal, Jorge; Wächter, Andreas; Waltz, Richard A. Adaptive barrier update strategies for nonlinear interior methods. (English) Zbl 1176.49036 SIAM J. Optim. 19, No. 4, 1674-1693 (2009). Summary: This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that heuristic adaptive choices, such as Mehrotra’s probing procedure, outperform monotone strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the minimization of a quality function. The paper also proposes a globalization framework that ensures the convergence of adaptive interior methods, and examines convergence failures of the Mehrotra predictor-corrector algorithm. The barrier update strategies proposed in this paper are applicable to a wide class of interior methods and are tested in the two distinct algorithmic frameworks provided by the IPOPT and KNITRO software packages. Cited in 23 Documents MSC: 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods 90C06 Large-scale problems in mathematical programming 90C30 Nonlinear programming 90C51 Interior-point methods Keywords:interior-point methods; barrier methods; nonlinear programming; constrained optimization Software:Ipopt; CUTEr; SifDec; KNITRO PDFBibTeX XMLCite \textit{J. Nocedal} et al., SIAM J. Optim. 19, No. 4, 1674--1693 (2009; Zbl 1176.49036) Full Text: DOI Link