Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T05:20:57.793Z Has data issue: false hasContentIssue false
  • English
  • Français

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).
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

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