Duality for multiobjective fractional programming problems involving d -type-I n-set functions

Authors

  • I.M. Stancu-Minasian The Romanian Academy, Institute of Mathematical Statistics and Applied Mathematics, Romania
  • Gheorghe Dogaru 'Mircea cel Bătrân', Naval Academy, Romania
  • Mădălina Andreea Stancu The Romanian Academy, Institute of Mathematical Statistics and Applied Mathematics, Romania

DOI:

https://doi.org/10.2298/YJOR0901063S

Keywords:

d-type-I set functions, multiobjective programming, duality results

Abstract

We establish duality results under generalized convexity assumptions for a multiobjective nonlinear fractional programming problem involving d -type-I n -set functions. Our results generalize the results obtained by Preda and Stancu-Minasian [24], [25].

References

Bector, C.R., Bhatia, D.P., Pandey, S. (1994) Duality for multiobjective fractional programming involving n-set functions. Journal of Mathematical Analysis and Applications, 186(3): 747

Bector, C.R., Bhatia, D., Pandey, S. (1994) Duality in nondifferentiable generalized fractional programming involving n-set functions. Utilitas Math, 45 91-96

Begis, D., Glowinski, R. (1975) Application de la méthode des éléments finis à l'approximation d'une probléme de domaine optimal: Méthodes de résolution de problémes approaches. Applied Mathematics & Optimization, 2(2): 130

Bhatia, D., Kumar, P. (1997) Pseudolinear vector optimization problems containing n-set functions. Indian J. Pure Appl. Math, 28 (4) 439-453

Bhatia, D., Mehra, A. (1999) Lagrange duality in multiobjective fractional programming problems with n-set functions. Journal of Mathematical Analysis and Applications, 236(2): 300

Bhatia, D., Mehra, A. (2001) Theorem of alternative for a class of quasiconvex n-set functions and its applications to multiobjective fractional programming problems. Indian J. Pure Appl. Math, 32 (6) 949-960

Bhatia, D., Tewari, S. (1993) Multiobjective fractional duality for n-set functions. J. Inform. Optim. Sci, 14 (3) 321-334

Cea, J., Gioan, A., Michel, J. (1973) Quelques résultats sur l'identification de domaines. Calcolo, 10 (3-4) 207-232

Corley, H.W. (1987) Optimization theory for n-set functions. Journal of Mathematical Analysis and Applications, 127(1): 193

Corley, H.W., Roberts, S.D. (1972) A partitioning problem with applications in regional design. Operations Research, 20(5): 1010

Dantzig, G., Wald, A. (1951) On the Fundamental Lemma of Neyman and Pearson. Annals of Mathematical Statistics, 22(1): 87

Jeyakumar, V., Mond, B. (1992) On generalised convex mathematical programming. J. Austral. Math. Soc., Ser. B, 34 (1) (1992) 43-53

Jo, C.L., Kim, D.S., Lee, G.M. (1994) Duality for multiobjective fractional programming involving n-set functions sup. Optimization, 29(3): 205

Kim, D.S., Lee, G.M., Jo, C.L. (1996) Duality theorems for multiobjective fractional minimization problems involving set functions. Southeast Asian Bull. Math, 20 (2) 65-72

Kim, D.S., Jo, C.L., Lee, G.M. (1998) Optimality and duality for multiobjective fractional programming involving n-set functions. Journal of Mathematical Analysis and Applications, 224(1): 1

Kumar, N., Budharaja, R.K., Mehra, A. (2004) Approximated efficiency for n-set multiobjective fractional programming. Asia-Pacific Journal of Operational Research, 21(2): 197

Mangasarian, O. (1969) Nonlinear programming. New York, itd: McGraw-Hill

Mishra, S.K. (2006) Duality for multiple objective fractional subset programming with generalized (F,ρ,σ,θ) - V -type-I functions. Journal of Global Optimization, 36(4): 499

Mishra, S.K., Wang, S.Y., Lai, K.K. (2006) Optimality and duality for a multi-objective programming problem involving generalized d-type-I and related n-set functions. European Journal of Operational Research, 173(2): 405

Morris, R.J.T. (1979) Optimal constrained selection of a measurable subset. Journal of Mathematical Analysis and Applications, 70(2): 546

Neuman, J., Person, F.S. (1933) On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society: Series A, 231, 289-337

Preda, V. (1995) On duality of multiobjective fractional measurable subset selection problems. Journal of Mathematical Analysis and Applications, 196(2): 514

Preda, V. (1998) Duality for multiobjective fractional programming problems involving n-set functions. u: Andreian Cazacu C., Lehto O., Rassias Th.M. [ur.] Analysis and Topology, World Scientific Publishing Company, 569-583

Preda, V., Stancu-Minasian, I.M. (2001) Optimality and Wolfe duality for multiobjective programming problems involving n-set functions. u: Hadjisavvas N., J.E. Martinez-Legaz, J.P. Penot [ur.] Generalized Convexity and Generalized Monotonocity, Proceedings of the 6th International Symposium on Generalized Convexity/ Monotonocity, Karlovassi, Samos, Greece, 25 Aug. -3 Sep. 1999., Lecture Not, Berlin: Springer-Verlag, str. 349-361

Preda, V., Stancu-Minasian, I.M. (2002) Mond-Weir duality for multiobjective programming problems involving d-type-I n-set functions. Rev. Roumaine Math. Pures Appl, 47 (4) 499-508

Preda, V., Stancu-Minasian, I.M., Koller, E. (2003) On optimality and duality for multiobjective programming problems involving generalized d-type-I and related n-set functions. Journal of Mathematical Analysis and Applications, 283(1): 114

Stancu-Minasian, I.M. (1997) Fractional programming theory, methods and applications. Dordrecht, The Netherlands: Kluwer Academic Publishers, pages, VIII + 418

Stancu-Minasian, I.M., Preda, V. (2002) Optimality conditions and duality for programming problems involving set and n-set functions: A survey. J. Statist. Manag. Systems, 5, (1-3), 175-207

Suneja, S.K., Srivastava, M.K. (1997) Optimality and duality in nondifferentiable multiobjective optimization involving d-type I and related functions. Journal of Mathematical Analysis and Applications, 206(2): 465

Wang, P.K.C. (1977) On a class of optimization problems involving domain variations. Lecture Notes in Control and Information Sciences, Berlin, vol. 2, 49-60, Springer-Verlag

Ye, Y. (1991) D-invexity and optimality conditions. Journal of Mathematical Analysis and Applications, 162(1): 242

Zalmai, G.J. (1991) Optimality conditions and duality for multiobjective measurable subset selection problems. Optimization, 22(2): 221

Zalmai, G.J. (2001) Semiparametric sufficient efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized (F,ρ,θ) -convex functions. Southeast Asian Bulletin of Mathematics, 25 (2), 529-563

Zalmai, G.J. (2002) Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized (F, ρ, σ, θ) - V -convex functions. Computers and Math. Appl, 43 1489-1520

Zalmai, G.J. (2003) Parametric sufficient efficiency conditions and duality models for multi-objective fractional subset programming problems with generalized (F, ρ, θ) -convex functions. J. Stat. Manag. Syst, 6, (2), 331-370

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Published

2009-03-01

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Research Articles