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Adaptive barrier update strategies for nonlinear interior methods. (English) Zbl 1176.49036

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.

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

Software:

Ipopt; CUTEr; SifDec; KNITRO
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