Sufficient optimality criteria and duality for nondifferentiable fractional variational problems with generalized (F, ρ)-convexity

References

• Bector , C.R. , Chandra , S. and Husain , I. 1992 . Generalized continuous fractional programming duality: a parametric approach . Util. Math , 42 : 39 – 60 .
   Web of Science ®Google Scholar
• Bector , C.R. , Chandra , S. and Kumar , V. 1994 . Duality for minmax programming involing V-invex functions . Optimization , 30 : 93 – 103 .
   Google Scholar
• Bector , C.R. and Husain , I. 1992 . Duality for multiobjective variational problems . J. Math. Anal. Appl , 166 : 214 – 229 .
   Web of Science ®Google Scholar
• Bhatia , D. and Jain , P. 1994 . Generalized (Fρ)-convexity and duality for nonsmooth multiobjective programs . Optimization , 31 : 153 – 164 .
   Google Scholar
• Bhatia , D. and Kumar , P. 1995 . Multiobjection control problem with generalized invexity . J. Math. Anal. Appl , 189 : 676 – 692 .
   Google Scholar
• Chandra , S. , Craven , B.D. and Husain , I. 1985 . Continuous programming containing arbitrary norms . J. Austral. Math. Soc. Ser. A , 39 : 28 – 38 .
   Google Scholar
• Chandra , S. , Craven , B.D. and Husain , I. 1985 . A class of nondifferentiable continuous programming problems . J. Math. Anal. Appl , 107 : 122 – 131 .
   Web of Science ®Google Scholar
• Chandra , S. , Craven , B.D. and Husain , I. 1988 . A class of nondifferentiable control problems . J. Optim Theory Appl , 56 : 227 – 243 .
   Google Scholar
• Gulati , T.R. 1994 . Sufficiency and duality in multiobjective programming involving generalized F-convex functions . J. Math. Anal. Appl , 183 : 181 – 195 .
   Web of Science ®Google Scholar
• Hanson , M.A. 1981 . On sufficiency of the Kuhn-Tucker conditions . J. Math. Anal. Appl , 80 : 545 – 550 .
   Web of Science ®Google Scholar
• Hanson , M.A. and Mond , B. 1982 . Further generalizations of convtxity in mathematical programming . J. Inf. Optim. Sci , 3 : 25 – 32 .
   Google Scholar
• Jeyakumar , V. and Mond , B. 1992 . On generalized convex mathematical programming . J. Austral. Math. Soc. Ser. B , 34 : 43 – 53 .
   Google Scholar
• Kaul , R.N. , Suneja , S.K. and Srivastava , M.K. 1994 . Optimality criteria and duality in multipleobjective optimization involving generalized invexity . J. Optim. Theory Appl , 80 : 465 – 482 .
   Web of Science ®Google Scholar
• Lai , H.C. and Liu , J.C. 1997 . Optimality conditions for multioniective programming with generalized -convex set functions . J. Math. Anal. Appl , 215 : 443 – 460 .
   Web of Science ®Google Scholar
• Lai H. C. Liu J. C. Sufficiency criteria and duality for complexnondifferentiable fractional programming Preprint
   Google Scholar
• Lal , S.N. , Nath , B. and Kumar , A. 1994 . Duality for some nondifferi:ntiable static multiobjective programming problems . J.Math. Anal. Appl , 186 : 862 – 867 .
   Web of Science ®Google Scholar
• Liu , J.C. 1996 . ϵ-Pareto optimality for nondifferentiable multiolljective programming ria penality function . J. Math. Anal. Appl , 198 : 248 – 261 .
   Web of Science ®Google Scholar
• Liu , J.C. 1996 . Optiimalitya nd duality for multiobjective fractional programming involving nonsmooth (F,ρ)-convex functions . Optimization , 36 : 333 – 346 .
   Google Scholar
• Liu , J.C. 1996 . Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions . Optimization , 37 : 27 – 39 .
   Google Scholar
• Liu , J.C. 1996 . Optimality and duality for generalized fractional variatonal problems involving generalized (F,ρ)-convex functions . Optimization , 37 : 369 – 383 .
   Google Scholar
• Liu , J.C. 1996 . Optimality and duality for generalized fractional programming involving nonsmooth (F,ρ)-convex functions . Comput. Math. and Appl , 32 : 91 – 102 .
   Web of Science ®Google Scholar
• Liu , J.C. 1996 . Duality for nondifferentiable static multiobjective variational problems involving generalized (F,ρ)-convex functions . Comput. Math. and Appl , 31 : 77 – 89 .
   Web of Science ®Google Scholar
• Liu , J.C. 1996 . Optimality and duality for generalized fractional programming involving nonsmooth pseudoinvex functions . J. Math. Anal. Appl , 202 : 667 – 685 .
   Web of Science ®Google Scholar
• Liu , J.C. 1997 . Optimality and duality for multiobjective programming involving subdifferentiable set functions . Optimization , 39 : 239 – 252 .
   Google Scholar
• Liu , J.C. 1997 . Sufficiency criteria and duality in complex nonlinear programming involving pseudoinvex function . Optimization , 39 : 123 – 135 .
   Google Scholar
• Mond , B. , Chandra , S. and Husain , I. 1988 . Duality for variational problems with invexity . J. Math. Anal. Appl , 134 : 322 – 328 .
   Web of Science ®Google Scholar
• Mond , B. and Husain , I. 1989 . Sufficient optimality criteria and duality for variational problems with generalized invexity . J. Austral. Math. Soc. Ser. B , 31 : 108 – 121 .
   Google Scholar
• Mond , B. and Smart , I. 1989 . Duality with invexity for a class of nondifferentiable static and continuous programming problems . J. Math. Anal. Appl , 141 : 373 – 388 .
   Web of Science ®Google Scholar
• Mond , B. and Weir , T. 1981 . Generalized concavity and duality, Generalized Concavity in Optimization and Economics , Edited by: Schaible , S. and Ziemba , W.T. 263 – 279 . New york : Academic Press .
   Google Scholar
• Mishra , S.K. and Mukherjee , R.N. 1994 . On efficiency and duality for multiobjective variational problems . J. Math. Anal. Appl , 187 : 40 – 45 .
   Web of Science ®Google Scholar
• Mishra , S.K. and Mukherjee , R.N. 1994 . Duality for multiobjective fractional variational problems . J. Math. Anal. Appl , 186 : 711 – 725 .
   Web of Science ®Google Scholar
• Preda , V. 1992 . On efficiency and duality for multiobjective programs . J. Math. Anal. Appl , 166 : 365 – 377 .
   Web of Science ®Google Scholar
• Preda , V. 1994 . On sufficiency and duality for generalized quasiconvex programs . J. Math. Anal. Appl , 181 : 77 – 88 .
   Web of Science ®Google Scholar
• Ponstein , J. 1969 . Seven kinds of convexity . SIAM Rev , 9 : 115 – 119 .
   Web of Science ®Google Scholar
• Vial , J.P. 1982 . Strong convexity of sets and functions . J. Math. Econ , 9 : 187 – 205 .
   Web of Science ®Google Scholar
• Vial , J.P. 1983 . Strong and weak convexity of sets and functions . Math. Oper. Res , 8 : 231 – 259 .
   Web of Science ®Google Scholar
• Zalmai , G.J. 1990 . Optimality conditions and duality for a class of continuoustime generalized fractional programming problems problems . J. Math. Anal. Appl , 153 : 356 – 371 .
   Web of Science ®Google Scholar
• Zalmai , G.J. 1985 . The Fritz John and Kuhn-Tucker optimality conditions in continuous-time nonlinear programming . J. Math. Anal. Appl , 110 : 503 – 518 .
   Web of Science ®Google Scholar
• Zalmai , G.J. 1994 . Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems . Optimization , 30 : 15 – 51 .
   Google Scholar
• Zalmai , G.J. 1994 . Proper efficiency and duality for a class of multiobjective fractional variational problems containing arbitrary norms . Optimization , 29 : 333 – 347 .
   Google Scholar
• Zalmai , G.J. 1995 . Proper efficiency condditions and duality models for constrained multiobjective variational problems containin arbitrary norms . J. Math. Anal. Appl , 196 : 411 – 427 .
   Google Scholar
• Zalmai , G.J. 1995 . Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and ρ-convex functions . Optimization , 32 : 95 – 124 .
   Google Scholar