Computational Optimization and Applications

, Volume 64, Issue 2, pp 327–354 | Cite as

An inertia-free filter line-search algorithm for large-scale nonlinear programming

  • Nai-Yuan Chiang
  • Victor M. Zavala


We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.


Inertia Nonlinear programming Filter line-search Nonconvex Large-scale 



This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract No. DE-AC02-06CH11357. We thank Frank Curtis and Jorge Nocedal for technical discussions. Victor M. Zavala acknowledges funding from the DOE Office of Science under the Early Career program. We also acknowledge the computing resources provided by the Laboratory Computing Resource Center at Argonne National Laboratory.

Supplementary material

10589_2015_9820_MOESM1_ESM.pdf (132 kb)
Supplementary material 1 (pdf 132 KB)


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Copyright information

© Springer Science+Business Media New York (Outside USA) 2016

Authors and Affiliations

  1. 1.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA
  2. 2.Department of Chemical and Biological EngineeringUniversity of Wisconsin-MadisonMadisonUSA

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