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Contribution to Dubovitskiy and Milyutin's optimization formalism

  • Ludmila Rigby
Mathematical Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)

Abstract

This paper is a contribution to the unified approach of Halkin, Neustadt, Gamkrelidze and others to the theory of necessary conditions for general optimization problems.

The basic problem is formulated in terms of real linear topological spaces, mappings between them and a partial ordering determined by a proper convex cone. It includes, therefore, problems with both scalar- and vector-valued optimality criteria.

Optimality conditions are developed in terms of Gâteaux and Fréchet differentials of given mappings and linear continuous functionals on the spaces concerned, making use of the Dubovitskiy and Milyutin's formalism.

Keywords

Banach Space Convex Cone SIAM Journal Separation Theorem Polar Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Ludmila Rigby
    • 1
  1. 1.Department of Computing and ControlImperial College of Science and TechnologyLondonUnited Kingdom

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