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Journal of Global Optimization

, Volume 40, Issue 1–3, pp 197–208 | Cite as

Constrained extremum problems with infinite dimensional image. Selection and saddle point

  • K. Madani
  • G. Mastroeni
  • A. Moldovan
Article

Abstract

The paper deals with Image Space Analysis for constrained extremum problems having infinite dimensional image. It is shown that the introduction of selection for point- to-set maps and of quasi-multipliers allows one to establish sufficient optimality conditions for problems, where the classic ones fail.

Keywords

Optimality conditions Saddle point Multipliers Quasi-multipliers Image Space Analysis 

Mathematics Subject Classification (2000)

90C 65K 

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References

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    Giannessi, F., Mastroeni, G., Uderzo, A.: A multifunction approach to extremum problems having infinite dimensional image: necessary conditions for unilateral constraints, pp. 39–51. Cybernetics and System Analysis, No. 3, Plenum (2002)Google Scholar
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    Hestenes M.R. (1966). Calculus of Variations and Optimal Control Theory. Wiley, New York Google Scholar
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    Madani, K., Mastroeni, G., Moldovan, A.: Constrained Extremum Problems with Infinite dimensional Image. Selection and Necessary Conditions. J. Optimiz. Theory App. 1 (135) N.1. (2007)Google Scholar
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    Pars L.A. (1962). An Introduction to the Calculus of Variations. Heinemann, London Google Scholar

Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OranOranAlgeria
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

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