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Full Stability of General Parametric Variational Systems

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Abstract

The paper introduces and studies the notions of Lipschitzian and Hölderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly verifiable sufficient conditions for, such full stability properties under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli. The obtained results are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    B. S. Mordukhovich & D. T. Pham

  2. RUDN University, Moscow, 117198, Russia

    B. S. Mordukhovich

  3. Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA

    T. T. A. Nghia

Authors
  1. B. S. Mordukhovich
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  2. T. T. A. Nghia
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  3. D. T. Pham
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Correspondence to B. S. Mordukhovich.

Additional information

Research of B. S. Mordukhovich and D. T. Pham was partly supported by the US National Science Foundation under grant DMS-1512846, by the US Air Force Office of Scientific Research under grant #15RT0462 and by the RUDN University Program 5-100.

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Mordukhovich, B.S., Nghia, T.T.A. & Pham, D.T. Full Stability of General Parametric Variational Systems. Set-Valued Var. Anal 26, 911–946 (2018). https://doi.org/10.1007/s11228-018-0474-7

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