Optimal sensitivity based on IPOPT

Abstract

We introduce a flexible, open source implementation that provides the optimal sensitivity of solutions of nonlinear programming (NLP) problems, and is adapted to a fast solver based on a barrier NLP method. The program, called sIPOPT evaluates the sensitivity of the Karush–Kuhn–Tucker (KKT) system with respect to perturbation parameters. It is paired with the open-source IPOPT NLP solver and reuses matrix factorizations from the solver, so that sensitivities to parameters are determined with minimal computational cost. Aside from estimating sensitivities for parametric NLPs, the program provides approximate NLP solutions for nonlinear model predictive control and state estimation. These are enabled by pre-factored KKT matrices and a fix-relax strategy based on Schur complements. In addition, reduced Hessians are obtained at minimal cost and these are particularly effective to approximate covariance matrices in parameter and state estimation problems. The sIPOPT program is demonstrated on four case studies to illustrate all of these features.

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Correspondence to Lorenz T. Biegler.

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Pirnay, H., López-Negrete, R. & Biegler, L.T. Optimal sensitivity based on IPOPT. Math. Prog. Comp. 4, 307–331 (2012). https://doi.org/10.1007/s12532-012-0043-2

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Keywords

  • NLP
  • Sensitivity
  • Interior point

Mathematics Subject Classification (2000)

  • 90C30
  • 90C31
  • 90C51
  • 90-08