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Optimality and Stability in Mathematical Programming pp 39–76Cite as

A unified theory of first and second order conditions for extremum problems in topological vector spaces

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Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 19))

Abstract

The paper studies an abstract optimization problem (P) in infinite dimensional spaces. From a general extremality condition, a variety of necessary conditions of first and second order, with or without differentiability assumptions, are derived for special cases of the general problem (P). Classical results are refined and new ones are added. Second order sufficient condition, under differentiability assumptions, are derived as well.

Research partly supported by the Technion and Deutsche Forschungsgemeinschaft.

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Author information

Authors and Affiliations

  1. Faculty of Industrial Engineering and Management Science, Technion, Israel Institute of Technology, Haifa, Israel

    A. Ben-Tal

  2. Institute of Mathematics, University of Bayreuth, Bayreuth, Federal Republic of Germany

    J. Zowe

Authors
  1. A. Ben-Tal
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  2. J. Zowe
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Editor information

Monique Guignard

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© 1982 The Mathematical Programming Society, Inc.

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Ben-Tal, A., Zowe, J. (1982). A unified theory of first and second order conditions for extremum problems in topological vector spaces. In: Guignard, M. (eds) Optimality and Stability in Mathematical Programming. Mathematical Programming Studies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120982

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  • DOI: https://doi.org/10.1007/BFb0120982

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00849-8

  • Online ISBN: 978-3-642-00850-4

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