Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T08:18:22.599Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiobjective symmetric duality with invexity

Published online by Cambridge University Press:  17 April 2009

T.R. Gulati ,
I. Husain  and
A. Ahmed
T.R. Gulati
Affiliation:
School of Basic & Applied SciencesThapar Institute of Engineering & TechnologyPatiala - 147 001India
I. Husain
Affiliation:
Department of MathematicsRegional Engineering CollegeHazratbal, Srinagar - 190 006India
A. Ahmed
Affiliation:
Department of Mathematics & StatisticsUniversity of KashmirHazratbal, Srinagar-190 006India
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.

Usual duality results are proved for Wolfe and Mond-Weir type multiobjective symmetric dual problems without nonnegativity constraints under invexity/generalised invexity assumptions. Moreover, assuming the kernel function to be skew symmetric, the multiobjective problems are exhibited to be self duals.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 25 - 36
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Borwein, J.M., Optimization with respect to partial ordering, D.Phil. Thesis (Oxford University, 1974).Google Scholar
[2]Chandra, S. and Husain, I., ‘Symmetric dual nondifferentiable programs’, Bull. Austral. Math. Soc. 24 (1981), 295–307.CrossRefGoogle Scholar
[3]Craven, B.D., ‘Lagrangian conditions and quasiduality’, Bull. Austral. Math. Soc. 16 (1977), 325–339.CrossRefGoogle Scholar
[4]Dantzig, G.B., Eisenberg, E. and Cottle, R.W., ‘Symmetric dual nonlinear programs’, Pacific J. Math 15 (1965), 809–812.CrossRefGoogle Scholar
[5]Dorn, W.S., ‘A symmetric dual theorem for quadratic programs’, J. Oper. Res. Soc. Japan 2 (1960), 93–97.Google Scholar
[6]Geoffrion, A.M., ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 618–630.CrossRefGoogle Scholar
[7]Hanson, M.A., ‘On sufficiency of the Kuhn-Tucker conditions’, J. Math. Anal. Appl. 80 (1981), 545–550.CrossRefGoogle Scholar
[8]Mond, B. and Cottle, R.W., ‘Self duality in mathematical programming’, SIAM J. Appl. Math. 14 (1966), 420–423.CrossRefGoogle Scholar
[9]Mond, B. and Hanson, M.A., ‘Symmetric duality for variational problems’, J. Math. Anal. Appl. 23 (1968), 161–172.CrossRefGoogle Scholar
[10]Mond, B. and Weir, T., ‘Generalized concavity and duality’, in Generalized concavity and duality in optimization and economics, (Schaible, S. and Ziemba, W.T., Editors) (Academic Press, New York, 1981), pp. 263–279.Google Scholar
[11]Smart, I. and Mond, B., ‘Symmetric duality with invexity in variational problems’, J. Math. Anal. Appl. 152 (1992), 536–545.CrossRefGoogle Scholar
[12]Weir, T. and Mond, B., ‘Symmetric and self duality in multiple objective programming’, Asia-Pacific J. Oper. Res. 5 (1988), 124–133.Google Scholar