Minimization and Mountain-Pass Theorems

  • Maria do Rosário Grossinho
  • Stepan Agop Tersian
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 52)


In this introductory chapter, we consider the concept on differentiability of mappings in Banach spaces, Fréchet and Gâteaux derivatives, secondorder derivatives and general minimization theorems. Variational principles of Ekeland [Ek1] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais—Smale conditions and mountain-pass theorems are considered. The deformation approach and ε—variational approach are applied to prove the mountainpass theorem and its various extensions.


Banach Space Convergent Subsequence Critical Point Theory Minimax Theorem Critical Point Theorem 
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.


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Maria do Rosário Grossinho
    • 1
    • 2
  • Stepan Agop Tersian
    • 3
  1. 1.ISEGUniversidade Técnica de LisboaPortugal
  2. 2.CMAFUniversidade de LisboaPortugal
  3. 3.University of RousseBulgaria

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