Abstract
A nonsmooth multiobjective programming problem is considered and Kuhn-Tucker type sufficient conditions are derived for properly efficiency solutions. Weak and strong duality results are established for Mon-Weir type dual. These results are obtained under generalized convexity assumptions.
Similar content being viewed by others
References
R.H. CLARKE, “Optimization and nonsmooth analysis”, Wiley-lnterscience, New York 1983.
B.D. CRAVEN, “Invex functions and constrained locak minima”, Bull. Austral. Math. Soc. 24 (1981), 357–366.
R.R. Egudo AND M.A. HANSON, “On sufficiency of Kuhn-tucker conditions in nonsmooth multiobjective programming”, FSU Technical Report Number M-888, 1993.
R.R. EGUDO, T. WEIR AND O. MOND, “Duality without constraint qualification for multiobjective programming”, J. Austral. Math. Soc. Series B 33 (1992), 531–544.
A.M. GEOFFRION, “Proper efficiency and the theory of vector maximization”, J. Math. Anal, Appl., 22 (1968), 618–630.
T.R. GULATI AND N. TALLT, “Sufficiency and duality in non-differentiable multiobjective programming:, Opsearch 28 (1991), 73–87.
M.A. HANSON AND B. MOND, “Necessary and sufficient conditions in constrained optimization, Math, Prog. 37 (1987), 51–58.
V. JEYAKUMAR, “Strong and Weak invexity in mathematical programming,” Methods Oper. Res 55 (1985), 109–125.
V. JEYAKUMAR AND B. Mond, “On generalized convex mathematical programming”, J. Austral. Math. Soc. Series B 39 (1992), 43–53.
R. KANNIAPPAAN AND S.M.A. Sastry, “Duality theorems and an optimality condition for nondifferentiable convex programming”, J. Austral. Math. Soc. Series A 32 (1988) 369–379.
H.C. LAI AND C.P. HO, “Duality theorem of non-differentiable convex multiobjective programming:, J. Optim. Theory Appl. 50 (1986), 407–420.
S.K. MISHRA AND R.N. Mukherjee. “On generalized convex multiobjective non-smooth programming”, J. Austral. Math. Soc, Ser B. 38 (1996), 140–148.
F. ZHAO, “On sufficiency of the Kuhn-Tucker conditions in non-differentiable program-ming”, Bull. Austral. Math. Soc. 46 (1992), 385–389.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mishra, S.K. On Sufficiency and Duration in Nonsmooth Multiobjective Programming. OPSEARCH 34, 221–231 (1997). https://doi.org/10.1007/BF03398527
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03398527