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Stability Analysis for Composite Optimization Problems and Parametric Variational Systems

Author

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  • B. S. Mordukhovich

    (Wayne State University
    RUDN University)

  • M. E. Sarabi

    (Miami University)

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.

Suggested Citation

  • B. S. Mordukhovich & M. E. Sarabi, 2017. "Stability Analysis for Composite Optimization Problems and Parametric Variational Systems," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 554-577, February.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-1039-2
    DOI: 10.1007/s10957-016-1039-2
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    References listed on IDEAS

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    1. B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
    2. B. S. Mordukhovich & T. T. A. Nghia & R. T. Rockafellar, 2015. "Full Stability in Finite-Dimensional Optimization," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 226-252, February.
    3. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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