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Stability Analysis for Composite Optimization Problems and Parametric Variational Systems

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Abstract

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise linear functions recently obtained by the authors. We mainly focus here on establishing relationships between full stability of local minimizers in composite optimization and Robinson’s strong regularity of associated (linearized and nonlinearized) KKT systems. Finally, we address Lipschitzian stability of parametric variational systems with convex piecewise linear potentials.

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Acknowledgements

This research was partly supported by the National Science Foundation under grants DMS-1007132 and DMS-1512846 and by the Air Force Office of Scientific Research grant #15RT0462. The authors are grateful to both anonymous referees for their valuable remarks, which helped us to improve the original presentation.

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Authors and Affiliations

  1. Wayne State University, Detroit, MI, USA

    B. S. Mordukhovich

  2. RUDN University, Moscow, Russia, 117198

    B. S. Mordukhovich

  3. Miami University, Oxford, OH, USA

    M. E. Sarabi

Authors
  1. B. S. Mordukhovich
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  2. M. E. Sarabi
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Correspondence to B. S. Mordukhovich.

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Communicated by Yurii Nesterov.

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Mordukhovich, B.S., Sarabi, M.E. Stability Analysis for Composite Optimization Problems and Parametric Variational Systems. J Optim Theory Appl 172, 554–577 (2017). https://doi.org/10.1007/s10957-016-1039-2

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  • DOI: https://doi.org/10.1007/s10957-016-1039-2

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