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Tangential extremal principles for finite and infinite systems of sets, I: basic theory

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Abstract

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization.

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References

  1. Borwein J.M., Zhu Q.J.: Techniques of Variational Analysis. Springer, New York (2005)

    MATH  Google Scholar 

  2. Goberna M.A., López M.A.: Linear Semi-Infinite Optimization. Wiley, Chichester (1998)

    MATH  Google Scholar 

  3. Kruger A.Y., Mordukhovich B.S.: Extremal points and the Euler equation in nonsmooth optimization. Dokl. Akad. Nauk BSSR 24, 684–687 (1980)

    MathSciNet  MATH  Google Scholar 

  4. Mordukhovich B.S.: Maximum principle in problems of time optimal control with nonsmooth constraints. J. Appl. Math. Mech. 40, 960–969 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  5. Mordukhovich B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory. Springer, Berlin (2006)

    Google Scholar 

  6. Mordukhovich B.S.: Variational Analysis and Generalized Differentiation, II: Applications. Springer, Berlin (2006)

    Google Scholar 

  7. Mordukhovich, B.S., Phan, H.M.: Tangential extremal principles for finite and infinite systems of sets, II: Applications to semi-infinite and multiobjective optimization. Math. Program. (2011). doi:10.1007/s10107-012-0550-y

  8. Rockafellar R.T., Wets R-J.: Variational Analysis. Springer, Berlin (1998)

    Book  MATH  Google Scholar 

  9. Schirotzek W.: Nonsmooth Analysis. Springer, Berlin (2007)

    Book  MATH  Google Scholar 

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Authors and Affiliations

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

    Boris S. Mordukhovich & Hung M. Phan

Authors
  1. Boris S. Mordukhovich
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  2. Hung M. Phan
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Corresponding author

Correspondence to Boris S. Mordukhovich.

Additional information

This research was partially supported by the US National Science Foundation under grants DMS-0603846 and DMS-1007132 and by the Australian Research Council under grant DP-12092508.

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Mordukhovich, B.S., Phan, H.M. Tangential extremal principles for finite and infinite systems of sets, I: basic theory. Math. Program. 136, 3–30 (2012). https://doi.org/10.1007/s10107-012-0549-4

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  • DOI: https://doi.org/10.1007/s10107-012-0549-4

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