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Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity

Author

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  • Francisco Facchinei

    (Department of Computer, Control, and Management Engineering Antonio Ruberti, Sapienza University of Rome, 00185 Rome, Italy)

  • Vyacheslav Kungurtsev

    (Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, 12135 Prague, Czech Republic)

  • Lorenzo Lampariello

    (Department of Business Studies, Roma Tre University, 00145 Rome, Italy)

  • Gesualdo Scutari

    (School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47097)

Abstract

We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only enter in the theoretical analysis of convergence while the algorithm itself is penalty free. Based on this idea, we are able to establish several new results, including the first general analysis for diminishing stepsize methods in nonconvex, constrained optimization, showing convergence to generalized stationary points, and a complexity study for sequential quadratic programming–type algorithms.

Suggested Citation

  • Francisco Facchinei & Vyacheslav Kungurtsev & Lorenzo Lampariello & Gesualdo Scutari, 2021. "Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 595-627, May.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:2:p:595-627
    DOI: 10.1287/moor.2020.1079
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    References listed on IDEAS

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    6. Alfred Auslender, 2013. "An Extended Sequential Quadratically Constrained Quadratic Programming Algorithm for Nonlinear, Semidefinite, and Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 183-212, February.
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