Ruixiong Tian, Zhe Xiang, et al.
Qinghua Daxue Xuebao/Journal of Tsinghua University
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. © 2009 Society for Industrial and Applied Mathematics.
Ruixiong Tian, Zhe Xiang, et al.
Qinghua Daxue Xuebao/Journal of Tsinghua University
Guo-Jun Qi, Charu Aggarwal, et al.
IEEE TPAMI
Sonia Cafieri, Jon Lee, et al.
Journal of Global Optimization
George Markowsky
J. Math. Anal. Appl.