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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 22, 1991 - Issue 4
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Original Articles

Invexity and generalized convexity

Rita Pini Dept. of Mathematics, University of Verona; Facoltà di Economia e Commercio Istituto di Matematica, Università degii Studi di Verona, Via del’Artigliere, 19, Verona, 37129, Italy
Pages 513-525 | Received 01 Dec 1990, Published online: 27 Jun 2007
 
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Abstract

Let f be a real differentiate function defined on the open subset A of R n;f is said to be invex if the following inequality is satisfied

for a suitable function η

The purpose of this paper is to investigate the relationship between invexity and generalized convexity; moreover, we shall give necessary and sufficient conditions for a differentiable function to be η-invex, which are natural extensions of the analogous conditions for convex functions.

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