Optimization Letters

, Volume 9, Issue 4, pp 769–777 | Cite as

Local maximum points of explicitly quasiconvex functions

Original Paper
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Abstract

This work concerns generalized convex real-valued functions defined on a nonempty convex subset of a real topological linear space. Its aim is twofold: first, to show that any local maximum point of an explicitly quasiconvex function is a global minimum point whenever it belongs to the intrinsic core of the function’s domain and second, to characterize strictly convex normed spaces by applying this property for a particular class of convex functions.

Keywords

Local maximum point Relative algebraic interior Convex function Explicitly quasiconvex function Strictly convex space Least squares problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Computing and MathematicsUniversity of DerbyDerbyUK
  2. 2.Faculty of Mathematics and Computer ScienceBabeş-Bolyai University of Cluj-NapocaCluj-NapocaRomania

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