An inertia-free filter line-search algorithm for large-scale nonlinear programming
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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.
KeywordsInertia 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.
- 4.Balay, S., Brown, J., Buschelman, K., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M., McInnes, L., Smith, B., Zhang, H.: PETSc Users Manual Revision 3.4 (2013)Google Scholar
- 14.Chiang, N., Petra, C.G., Zavala, V.M.: Structured nonconvex optimization of large-scale energy systems using PIPS-NLP. In: Proceedings of the 18th Power Systems Computation Conference (PSCC). Wroclaw, Poland (2014)Google Scholar
- 21.Duff, I.S., Reid, J.K.: MA27—A Set of Fortran Subroutines for Solving Sparse Symmetric Sets of Linear Equations. UKAEA Atomic Energy Research Establishment (1982)Google Scholar
- 26.Haverbeke, N., Diehl, M., De Moor, B.: A structure exploiting interior-point method for moving horizon estimation. In: Proceedings of the 48th IEEE Conference on Decision and Control, pp. 1273–1278. IEEE (2009)Google Scholar
- 29.Heroux, M.A., Willenbring, J.M.: Trilinos Users Guide. Citeseer (2003)Google Scholar
- 32.Lubin, M., Petra, C.G., Anitescu, M., Zavala, V.M.: Scalable stochastic optimization of complex energy systems. In: International Conference for High Performance Computing, Networking, Storage and Analysis (SC), 2011, pp. 1–10. IEEE (2011)Google Scholar