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Generalized Extreme Elements

In: Generalized Solutions of Operator Equations and Extreme Elements

Author

Listed:
  • D. A. Klyushin

    (Kyiv National Taras Shevchenko University)

  • S. I. Lyashko

    (Kyiv National Taras Shevchenko University)

  • D. A. Nomirovskii

    (Kyiv National Taras Shevchenko University)

  • Yu. I. Petunin

    (Kyiv National Taras Shevchenko University)

  • V. V. Semenov

    (Kyiv National Taras Shevchenko University)

Abstract

Chapter is devoted to the concept of generalized solution of extreme problems. In Sect. 8.1 we give necessary motivations and the definition of generalized extreme element of bounded continuous functional defined of a bounded closed subset of a Banach space. In Sect. 8.2 we prove the theorem on existence of the generalized extreme element of a linear continuous functional. In Sect. 8.3 we study an interest issue concerning the possibility of compact dense embedding of linear normed space in Banach one. The purpose of Sects. 8.4 and 8.5 is to develop the theory of generalized solvability of convex minimization problems in infinite-dimensional Banach spaces.

Suggested Citation

  • D. A. Klyushin & S. I. Lyashko & D. A. Nomirovskii & Yu. I. Petunin & V. V. Semenov, 2012. "Generalized Extreme Elements," Springer Optimization and Its Applications, in: Generalized Solutions of Operator Equations and Extreme Elements, edition 1, chapter 0, pages 163-194, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0619-8_8
    DOI: 10.1007/978-1-4614-0619-8_8
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