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pySLEQP: A Sequential Linear Quadratic Programming Method Implemented in Python

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Modeling, Simulation and Optimization of Complex Processes HPSC 2015

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Abstract

We present a prototype implementation of a Sequential Linear Equality-Constrained Qudratic Programming (SLEQP) method for solving the nonlinear programming problem. Similar to SQP active set methods, SLEQP methods are iterative Newton-type methods. In every iteration, a trust region constrained linear programming problem is solved to estimate the active set. Subsequently, a trust region equality constrained quadratic programming problem is solved to obtain a step that promotes locally superlinear convergence. This class of methods has several appealing properties for future research in large-scale nonlinear programming. Implementations of SLEQP methods accessible for research, however, are scarcely found. To this end, we present pySLEQP, an implementation of an SLEQP method in Python. The performance and robustness of the method and our implementation are assessed using the CUTEst and CUTEr benchmark collections of nonlinear programming problems. pySLEQP is found to show robust behavior and reasonable performance.

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Acknowledgements

F. L. and C. K. were supported by DFG Graduate School 220 funded by the German Excellence Initiative. Financial support by the German Federal Ministry of Education and Research, grant no 05M2013-GOSSIP, by the European Union within the seventh Framework Programme under Grant Agreement no 611909, and by German Research Foundation within DFG project no BO364/19-1 is gratefully acknowledged. F. L. gratefully acknowledges funding by the German National Academic Foundation.

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Authors and Affiliations

  1. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany

    Felix Lenders & Hans Georg Bock

  2. Institut für Mathematische Optimierung, Technische Universität Carolo-Wilhelmina zu Braunschweig, Am Fallersleber Tore 1, 38100, Braunschweig, Germany

    Christian Kirches

Authors
  1. Felix Lenders
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  2. Christian Kirches
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  3. Hans Georg Bock
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Corresponding author

Correspondence to Felix Lenders .

Editor information

Editors and Affiliations

  1. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany

    Hans Georg Bock

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Hoang Xuan Phu

  3. Institute of Applied Mathematics, Heidelberg University, Heidelberg, Germany

    Rolf Rannacher

  4. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany

    Johannes P. Schlöder

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Lenders, F., Kirches, C., Bock, H.G. (2017). pySLEQP: A Sequential Linear Quadratic Programming Method Implemented in Python. In: Bock, H., Phu, H., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes HPSC 2015 . Springer, Cham. https://doi.org/10.1007/978-3-319-67168-0_9

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