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A note on the relationships between convexity and invexity

Published online by Cambridge University Press:  17 February 2009

Giorgio Giorgi
Giorgio Giorgi
Affiliation:
Department of Management Researches, Section of General and Applied Mathematics, University of Pavia, 27100 Pavia (Italy).
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Abstract

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Using the fact that a differentiable quasi-convex function is also pseudo-convex at every point x of its domain where ∇f(x) ≠ 0 recent results relating different forms of convexity and invexity are strengthened.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 1 , July 1990, pp. 97 - 99
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Ben-Israel, A. and Mond, B., “What is invexity?”, J Austral. Math. Soc. Ser. B 28 (1986) 1–9.CrossRefGoogle Scholar
[2] Craven, B. D. and Glover, B. M., “Invex functions and duality”, J. Austral. Math. Soc. Ser. A 39 (1985) 1–20.CrossRefGoogle Scholar
[3] Crouzeix, J. P. and Ferland, J. A., “Criteria for quasiconvexity and pseudoconvexity: relationships and comparisons”, Math. Programming 23 (1982) 193–205.CrossRefGoogle Scholar
[4] Jeyakumar, V., “Strong and weak invexity in mathematical programming”, Methods Oper. Res. 55 (1985) 109–125.Google Scholar
[5] Mangasarian, O. L., Nonlinear Programming (McGraw-Hill, New York, 1969).Google Scholar