Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-25T03:48:27.590Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimality and duality without a constraint qualification for minimax programming

Published online by Cambridge University Press:  17 April 2009

Houchun Zhou  and
Wenyu Sun
Houchun Zhou
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, Jiangsu, Peoples Republic of China and Department of Mathematics, Linyi Teacher's College, Linyi 276005, Shandong, Peoples Republic of China, e-mail: zhouhouchun@263.net
Wenyu Sun
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, Jiangsu, Peoples Republic of China, e-mail: wysun@pine.njnu.edu.cn
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.

Without the need of a constraint qualification, we establish the optimality necessary and sufficient conditions for generalised minimax programming. Using these optimality conditions, we construct a parametric dual model and a parameter-free mixed dual model. Several duality theorems are established.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 121 - 130
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Bector, C.R., Chandra, S. and Abha, , ‘On mixed duality in mathematical programming’, J. Math. Anal. Appl. 259 (2001), 346–356.CrossRefGoogle Scholar
[2]Ben-Israel, A., Ben-Tal, and Zlobec, S., Optimality in nonlinear programming: A feasible direction approach (John Wiley and Sons, New York, 1981).Google Scholar
[3]Crouzeix, J.P., Ferland, J.A. and Schaible, S., ‘Duality in generalized fractional programming’, Math. Programming 27 (1983), 342–354.CrossRefGoogle Scholar
[4]Egudo, R.R., Weir, T. and Mond, B., ‘Duality without a constriant qualification in multi-objective programming’, J. Austral. Math. Soc. Ser. B 33 (1992), 531–544.CrossRefGoogle Scholar
[5]Hiriart-Urruty, J.B. and Lemaréchal, C., Convex analysis and minimization algorithms I, Fundamental Principals of Mathematical Sciences 305 (Springer-Verlag, Berlin, Heidelberg, 1993).CrossRefGoogle Scholar
[6]Lai, H.C., Liu, J.C. and Tanaka, K., ‘Duality without a constriant qualification for minimax fractional programming’, J. Optim. Theory Appl 101 (1999), 109–125.CrossRefGoogle Scholar
[7]Mond, T. and Zlobec, S., ‘Duality for nondifferentible programming without a constirant qualification’, Utilitas Math. 15 (1979), 291–302.Google Scholar
[8]Weir, T. and Mond, B., ‘Duality generalized programming without a constriant qualification’, Utilitas Math. 31 (1987), 233–242.Google Scholar
[9]Weir, T. and Mond, B., ‘Duality for fractional programming without a constriant qualification’, Utilitas Math. 38 (1990), 41–55.Google Scholar