Abstract
In this paper, sufficient optimality conditions for a multiobjective subset programming problem are established under generalized \((\mathcal{F}, \alpha, \rho, d)\)-type-I functions.
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Bector C.R., Bhatia D. and Pandey S. (1994). Efficiency and duality for nonlinear multiobjective programs involving n-set functions. J. Math. Anal. Appl. 182: 486–500
Bector C.R., Bhatia D. and Pandey S. (1994). Duality for multiobjective fractional programming involving n-set functions. J. Math. Anal. Appl. 186: 747–768
Bector C.R. and Singh M. (1997). Duality for minmax b-vex programming involving n-set functions. J. Math. Anal. Appl. 215: 112–131
Begis D. and Glowinski R. (1975). Application de la méthode des éléments fini á l’approximation d’une probléme de domaine optimal, Méthodes de résolution de problémes approchés. Appl. Math. Optim. 2: 130–169
Bhatia D. and Kumar P. (1997). A note on fractional minmax programs containing n-set functions. J. Math. Anal. Appl. 215: 283–293
Bhatia D. and Mehra A. (1999). Lagrange duality in multiobjective fractional programming problems with n-set functions. J. Math. Anal. Appl. 236: 300–311
Cea J., Gioan A. and Michel J. (1973). Quelque résultats sur l’identification de domaines. Calcolo 10: 133–145
Chou J.H., Hsia W.S. and Lee T.Y. (1985). On multiple objective programming problems with set functions. J. Math. Anal. Appl. 105: 383–394
Corley H.W. (1987). Optimization theory for n-set functions. J. Math. Anal. Appl. 127: 193–205
Corley H.W. and Roberts S.D. (1972). A partitioning problem with applicationas in regional design. Oper. Res. 20: 1010–1019
Corley H.W. and Roberts S.D. (1972). Duality relationships for a partitioning problem. SIAM J. Appl. Math. 23: 490–494
Dantzig G. and Wald A. (1951). On the fundamental lemma of Neyman and Pearson. Ann. Math. Stat. 22: 87–93
Geoffrion A.M. (1968). Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22: 618–630
Hachimi M. and Aghezzaf B. (2004). Sufficiency and duality in differentiable multiobjective programming involving generalized type-I functions. J. Math. Anal. Appl. 296: 382–392
Hanson M.A. and Mond B. (1987). Necessary and sufficient conditions in constrained optimization. Math. Program. 37: 51–58
Jo C.L., Kim D.S. and Lee G.M. (1994). Duality for multiobjective fractional programming involving n-set functions. Optimization 29: 45–54
Kaul R.N., Suneja S.K. and Srivastava M.K. (1994). Optimality criteria and duality in multiobjective optimization involving generalized invexity. J. Optim. Theory Appl. 80: 465–482
Kim D.S., Jo C.L. and Lee G.M. (1998). Optimality and duality for multiobjective fractional programming involving n-set functions. J. Math. Anal. Appl. 224: 1–13
Lai H.C. and Liu J.C. (1999). Duality for a minmax programming problem containing n-set functions. J. Math. Anal. Appl. 229: 587–604
Liang Z.A., Huang H.X. and Pardalos P.M. (2001). Optimality conditions and duality for a class of nonlinear fractional programming problems. J. Optim. Theory Appl. 110(3): 611–619
Liang Z.A., Huang H.X. and Pardalos P.M. (2003). Efficiency conditions and duality for a class of multiobjective fractional programming problems. J. Glob. Optim. 27: 447–471
Lin L.J. (1990). Optimality of differentiable vector-valued n-set functions. J. Math. Anal. Appl. 149: 255–270
Mishra S.K. (2006) Duality for multiple objective fractional subset programming with generalized \((\mathcal{F}, \rho, \sigma, \theta)\)-V-type-I functions. J. Glob. Optim. 36:499–516
Morris R.J.T. (1979). Optimal constrained selection of a measurable set. J. Math. Anal. Appl. 70: 546–562
Neyman J. and Pearson E.S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. R. Soc. Lond. Ser. A 231: 289–337
Preda V. (1991). On minmax programming problems containing n-set functions. Optimization 22: 527–537
Preda V., Stancu-Minasian I.M. and Koller E. (2003). On optimality and duality for multiobjective programming problems involving generalized d-type-I and related n-set functions. J. Math. Anal. Appl. 283: 114–128
Wang, P.K.C.: On a class of optimization problems involving domain variations. In: Lecture Notes in Control and Information Sciences 2. Springer, Berlin (1977)
Zalmai G.J. (1991). Optimality conditions and duality for multiobjective measurable subset selection problems. Optimization 22(2): 221–238
Zalmai G.J. (1990). Sufficiency criteria and duality for nonlinear programs involving n-set functions. J. Math. Anal. Appl. 149: 322–338
Zalmai G.J. (2002) Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized \((\mathcal{F}, \alpha, \rho, \theta)\)-V-convex functions. Comput. Math. Appl. 43(12):1489–1520
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Ahmad, I., Sharma, S. Sufficiency in multiobjective subset programming involving generalized type-I functions. J Glob Optim 39, 473–481 (2007). https://doi.org/10.1007/s10898-007-9150-4
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DOI: https://doi.org/10.1007/s10898-007-9150-4