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Journal of Optimization Theory and Applications

, Volume 26, Issue 4, pp 533–568 | Cite as

Higher-order necessary conditions in abstract mathematical programming

  • K. H. Hoffmann
  • H. J. Kornstaedt
Contributed Papers

Abstract

We prove necessary extremum conditions for general nonlinear optimization problems in ordered topological vector spaces. For that reason, we define variational derivatives of higher order and introduce proper variations. Especially assuming certain weak hypotheses, we establish maximum principles of higher order.

Key Words

Optimization theory variational sets variational derivatives necessary conditions maximum principles 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • K. H. Hoffmann
    • 1
  • H. J. Kornstaedt
    • 2
  1. 1.III. Mathematisches InstitutFreie Universität BerlinBerlinGermany
  2. 2.Fachbereich MathematikTechnische Universität BerlinBerlinGermany

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