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Optimality Conditions for Several Types of Efficient Solutions of Set-Valued Optimization Problems

In: Nonlinear Analysis and Variational Problems

Author

Listed:
  • T.X.D. Ha

    (Hanoi Institute of Mathematics)

Abstract

A simple unified framework is presented for the study of strong efficient solutions, weak efficient solutions, positive proper efficient solutions, Henig global proper efficient solutions, Henig proper efficient solutions, super efficient solutions, Benson proper efficient solutions, Hartley proper efficient solutions, Hurwicz proper efficient solutions and Borwein proper efficient solutions of set-valued optimization problem with/or without constraints. Some versions of the Lagrange claim, the Fermat rule and the Lagrange multiplier rule are formulated in terms of the first- and second-order radial derivatives, the Ioffe approximate coderivative and the Clarke coderivative.

Suggested Citation

  • T.X.D. Ha, 2010. "Optimality Conditions for Several Types of Efficient Solutions of Set-Valued Optimization Problems," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias & Akhtar A. Khan (ed.), Nonlinear Analysis and Variational Problems, chapter 0, pages 305-324, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-0158-3_21
    DOI: 10.1007/978-1-4419-0158-3_21
    as

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