Abstract

The paper surveys several convexity concepts, referring to sets and to functions respectively, with the purpose to put them in some kind of order according to the same principle. First it examines the connections between six convexity concepts regarding sets in topological linear spaces and points out the most general concept among these concepts. On the basis of this analysis it is then revealed that twelve convexity concepts concerning functions, that take values in topological linear spaces, can be naturally defined by reduction to the investigated convexities for sets. The most general convexity concept for functions is also found. It is applied to establish an alternative theorem as well as necessary optimality conditions for weak multiobjective optimization problems.

Author information

Contact details are reproduced from the original publication and may be historical.

Wolfgang W. Breckner

Babeș-Bolyai University, Faculty of Mathematics and Computer Science, Str. Kogălniceanu Nr. 1, 3400 Cluj-Napoca, Romania.

Gábor Kassay

Babeș-Bolyai University, Faculty of Mathematics and Computer Science, Str. Kogălniceanu Nr. 1, 3400 Cluj-Napoca, Romania.

Keywords

  • Generalized convex sets
  • generalized convex functions
  • necessary optimality conditions

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Suggested citation

W. W. Breckner, G. Kassay. “A Systematization of Convexity Concepts for Sets and Functions.” Journal of Convex Analysis 4 (1997), No. 1, 109–127. https://doi.org/10.68381/jca04005

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Published by Heldermann Verlag, 1997. Rights now held by Banach Press LLC.