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Sequential quadratic programming methods for parametric nonlinear optimization

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Abstract

Sequential quadratic programming (SQP) methods are known to be efficient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties—a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers contain elements to enforce global convergence that can interfere with the potential to take advantage of these theoretical local properties in full. We present two new predictor–corrector procedures for solving a nonlinear program given a sufficiently accurate estimate of the solution of a similar problem. The procedures attempt to trace a homotopy path between solutions of the two problems, staying within the local domain of convergence for the series of problems generated. We provide theoretical convergence and tracking results, as well as some numerical results demonstrating the robustness and performance of the methods.

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Acknowledgments

We would like to thank Greg Horn for insightful discussions in regards to some of the details of the numerical software implementation of the algorithms, in particular with regards to parallelization. In addition, we’d like to thank the reviewers for their helpful suggestions for improving the presentation of the material in the paper. This research was supported by Research Council KUL: PFV/10/002 Optimization in Engineering Center OPTEC, GOA/10/09 MaNet and GOA/10/11 Global real-time optimal control of autonomous robots and mechatronic systems. Flemish Government: IOF/KP/SCORES4CHEM, FWO: PhD/postdoc Grants and projects: G.0320.08 (convex MPC), G.0377.09 (Mechatronics MPC); IWT: PhD Grants, projects: SBO LeCoPro; Belgian Federal Science Policy Office: IUAP P7 (DYSCO, Dynamical systems, control and optimization, 2012-2017); EU: FP7-EMBOCON (ICT- 248940), FP7-SADCO ( MC ITN-264735), FP7-TEMPO, ERC ST HIGHWIND (259 166), Eurostars SMART, ACCM.

It was also supported by the European social fund within the framework of realizing the project “Support of inter-sectoral mobility and quality enhancement of research teams at the Czech Technical University in Prague”, CZ.1.07/2.3.00/30.0034.

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Authors and Affiliations

  1. Department of Computer Science and Optimization in Engineering Center (OPTEC), KU Leuven, Celestijnenlaan 200A, 3001, Leuven-Heverlee, Belgium

    Vyacheslav Kungurtsev

  2. Department of Computer Science, Agent Technology Center, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic

    Vyacheslav Kungurtsev

  3. Department of Microsystems Engineering IMTEK, University of Freiburg, Georges-Koehler-Allee 102, 79110, Freiburg, Germany

    Moritz Diehl

  4. Electrical Engineering Department (ESAT-STADIUS) and Optimization in Engineering Center (OPTEC), KU Leuven, Kasteelpark Arenberg 10, 3001, Leuven-Heverlee, Belgium

    Moritz Diehl

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  1. Vyacheslav Kungurtsev
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Correspondence to Vyacheslav Kungurtsev.

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Kungurtsev, V., Diehl, M. Sequential quadratic programming methods for parametric nonlinear optimization. Comput Optim Appl 59, 475–509 (2014). https://doi.org/10.1007/s10589-014-9696-2

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