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Original Articles

Second-Order Parameter-Free Duality Models in Semi-Infinite Minmax Fractional Programming

Pages 1265-1298 | Received 08 Apr 2012, Accepted 01 Jan 2013, Published online: 25 Sep 2013

REFERENCES

  • B. Aghezzaf ( 2003 ). Second order mixed type duality in multiobjective programming problems . J. Math. Anal. Appl. 285 : 97 – 106 .
  • I. Ahmad and Z. Husain ( 2005 ). Nondifferentiable second-order symmetric duality . Asia-Pacific J. Oper. Res. 22 : 19 – 31 .
  • I. Ahmad and Z. Husain ( 2006 ). Second order (F, α, ρ, d)-convexity and duality in multiobjective programming . Inform. Sci. 176 : 3094 – 3103 .
  • I. Ahmad , Z. Husain , and S. Sharma ( 2007 ). Higher-order duality in nondifferentiable multiobjective programming . Numer. Func. Anal. Optim. 28 : 989 – 1002 .
  • I. Ahmad and S. Sharma ( 2007 ). Second-order duality for nondifferentiable multiobjective programming problems . Numer. Func. Anal. Optim. 28 : 975 – 988 .
  • C. R. Bector and B. K. Bector ( 1986 ). (Generalized) bonvex functions and second-order duality for a nonlinear programming problem . Congressus Numer. 22 : 37 – 52 .
  • C. R. Bector and B. K. Bector ( 1986 ). On various duality theorems for second-order duality in nonlinear programming . Cahiers Centre d’Études Rech. Opér. 28 : 283 – 292 .
  • C. R. Bector and S. Chandra ( 1986 ). Second-order duality for generalized fractional programming . Methods Oper. Res. 56 : 11 – 28 .
  • C. R. Bector and S. Chandra ( 1986 ). Second order symmetric and self dual programs . Opsearch 23 : 89 – 95 .
  • C. R. Bector and S. Chandra ( 1986 ). First and second order duality for a class of nondifferentiable fractional programming problems . J. Inform. Optim. Sci. 7 : 335 – 348 .
  • C. R. Bector and S. Chandra ( 1987 ). (Generalized) bonvexity and higher order duality for fractional programming . Opsearch 24 : 143 – 154 .
  • C. R. Bector , S. Chandra , S. Gupta , and S. K. Suneja ( 1994 ). Univex sets, functions, and univex nonlinear programming . In Generalized Convexity ( S. Komlósi , T. Rapcsák , and S. Schaible , Eds.). Springer-Verlag , New York , pp. 3 – 19 .
  • C. R. Bector , S. Chandra , and I. Husain ( 1991 ). Second-order duality for a minimax programming problem . Opsearch 28 : 249 – 263 .
  • X. Chen ( 2008 ). Sufficient conditions and duality for a class of multiobjective fractional programming problems with higher-order (F, α, ρ, d)-convexity . J. Appl. Math. Comput. 28 : 107 – 121 .
  • B. D. Craven ( 1981 ). Invex functions and constrained local minima . Bull. Austral. Math. Soc. 24 : 357 – 366 .
  • R. R. Egudo and M. A. Hanson ( 1993 ). Second order duality in multiobjective programming . Opsearch 30 : 223 – 230 .
  • T. R. Gulati and D. Agarwal ( 2007 ). Second-order duality in multiobjective programming involving (F, α, ρ, d)-V-type I functions . Numer. Funct. Anal. Optim. 28 : 1263 – 1277 .
  • T. R. Gulati and D. Agarwal ( 2007 ). On Huard type second-order converse duality in nonlinear programming . Appl. Math. Lett. 20 : 1057 – 1063 .
  • T. R. Gulati and D. Agarwal ( 2008 ). Optimality and duality in nondifferentiable mutliobjective mathematical programming involving higher order (F, α, ρ, d)-type I functions . J. Appl. Comput. 27 : 345 – 364 .
  • T. R. Gulati and I. Ahmad ( 1997 ). Second order symmetric duality for nonlinear minimax mixed integer programming problems . European J. Oper. Res. 101 : 122 – 129 .
  • T. R. Gulati , I. Ahmad , and I. Husain (2001). Second order symmetric duality with generalized convexity. Opsearch 38:210–222.
  • T. R. Gulati and Geeta ( 2010 ). Mond-Weir type second-order symmetric duality in multiobjective programming over cones . Appl. Math. Lett. 23 : 466 – 471 .
  • T. R. Gulati and S. K. Gupta ( 2007 ). Second-order symmetric duality for minimax integer programs over cones . Internat. J. Oper. Res. 4 : 181 – 188 .
  • T. R. Gulati and S. K. Gupta ( 2007 ). Higher-order nondifferentiable symmetric duality with generalized F-convexity . J. Math. Anal. Appl. 329 : 229 – 237 .
  • T. R. Gulati and S. K. Gupta ( 2007 ). A note on Mond-Weir type second-order symmetric duality . Asia-Pac. J. Oper. Res. 24 : 737 – 740 .
  • T. R. Gulati and S. K. Gupta ( 2009 ). Higher-order symmetric duality with cone constraints . Appl. Math. Lett. 22 : 776 – 781 .
  • T. R. Gulati , S. K. Gupta , and I. Ahmad ( 2008 ). Second-order symmetric duality with cone constraints . J. Comput. Appl. Math. 220 : 347 – 354 .
  • T. R. Gulati and G. Mehndiratta ( 2010 ). Nondifferentiable multiobjective Mond-Weir type second-order symmetric duality over cones . Optim. Lett. 4 : 293 – 309 .
  • T. R. Gulati , H. Saini , and S. K. Gupta ( 2010 ). Second-order multiobjective symmetric duality with cone constraints . European J. Oper. Res. 205 : 247 – 252 .
  • S. K. Gupta and N. Kailey ( 2010 ). A note on multiobjective second-order symmetric duality . European J. Oper. Res. 201 : 649 – 651 .
  • M. Hachimi and B. Aghezzaf ( 2004 ). Second order duality in multiobjective programming involving generalized type-I functions . Numer. Funct. Anal. Optim. 25 : 725 – 736 .
  • M. A. Hanson ( 1981 ). On sufficiency of the Kuhn-Tucker conditions . J. Math. Anal. Appl. 80 : 545 – 550 .
  • M. A. Hanson ( 1993 ). Second order invexity and duality in mathematical programming . Opsearch 30 : 313 – 320 .
  • M. A. Hanson and B. Mond ( 1982 ). Further generalizations of convexity in mathematical programming . J. Inform. Optim. Sci. 3 : 25 – 32 .
  • S. H. Hou and X. M. Yang ( 2001 ). On second-order symmetric duality in nondifferentiable programming . J. Math. Anal. Appl. 255 : 491 – 498 .
  • Z. Husain , I. Ahmad , and S. Sharma ( 2009 ). Second order duality for minmax fractional programming . Optim. Lett. 3 : 277 – 286 .
  • I. Husain , A. Goyel , and M. Masoodi ( 2007 ). Second order symmetric and maxmin symmetric duality with cone constraints . Internat. J. Oper Res. 4 : 199 – 205 .
  • I. Husain and Z. Jabeen ( 2004 ). Second order duality for fractional programming with support functions . Opsearch 41 : 121 – 134 .
  • V. Jeyakumar ( 1985 ). ρ-Convexity and second order duality . Utilitas Math. 29 : 71 – 85 .
  • V. Jeyakumar ( 1985 ). First and second order fractional programming duality . Opsearch 22 : 24 – 41 .
  • V. Jeyakumar ( 1985 ). Strong and weak invexity in mathematical programming . Opsearch 55 : 109 – 125 .
  • P. Kanniappan and Pandian ( 1996 ). On generalized convex functions in optimization theory – A survey . Opsearch 33 : 174 – 185 .
  • J. C. Liu ( 1999 ). Second order duality for minimax programming . Utilitas Math. 56 : 53 – 63 .
  • O. L. Mangasarian ( 1975 ). Second- and higher-order duality theorems in nonlinear programming . J. Math. Anal. Appl. 51 : 607 – 620 .
  • S. K. Mishra ( 1997 ). Second order generalized invexity and duality in mathematical programming . Optimization 42 : 51 – 69 .
  • S. K. Mishra ( 2000 ). Second order symmetric duality in mathematical programming with F-convexity . European J. Oper. Res. 127 : 507 – 518 .
  • S. K. Mishra and N. G. Rueda ( 2000 ). Higher-order generalized invexity and duality in mathematical programming . J. Math. Anal. Appl. 247 : 173 – 182 .
  • S. K. Mishra and N. G. Rueda ( 2006 ). Second-order duality for nondifferentiable minimax programming involving generalized type I functions . J. Optim. Theory Appl. 130 : 477 – 486 .
  • B. Mond ( 1974 ). Second order duality for nonlinear programs . Opsearch 11 : 90 – 99 .
  • B. Mond and T. Weir ( 1981 ). Generalized convexity and higher-order duality . J. Math. Sci. 16 : 74 – 94 .
  • B. Mond and T. Weir (1981). Generalized concavity and duality. In Generalized Concavity in Optimization and Economics ( S. Schaible and W. T. Ziemba , Eds.). Academic Press , New York, pp. 263–279.
  • B. Mond and J. Zhang ( 1995 ). Duality for multiobjective programming involving second-order V-invex functions . In Proceedings of the Optimization Miniconference II ( B. M. Glover and V. Jeyakumar , Eds.). University of New South Wales , Sydney , Australia , pp. 89 – 100 .
  • B. Mond and J. Zhang ( 1998 ). Higher order invexity and duality in mathemaical programming . In Generalized Convexity, Generalized Monotonicity: Recent Results ( J. P. Crouzeix et al., Eds.). Kluwer Academic , the Netherlands , pp. 357 – 372 .
  • R. B. Patel ( 1997 ). Second order duality in multiobjective fractional programming . Indian J. Math. 38 : 39 – 46 .
  • R. Pini and C. Singh ( 1997 ). A survey of recent [1985–1995] advances in generalized convexity with applications to duality theory and optimality conditions . Optimization 39 : 311 – 360 .
  • M. K. Srivastava and M. Bhatia ( 2006 ). Symmetric duality for multiobjective programming using second order (F, ρ)-convexity . Opsearch 43 : 274 – 295 .
  • M. K. Srivastava and M. G. Govil ( 2000 ). Second order duality for multiobjective programming involving (F, ρ, σ)-type I functions . Opsearch 37 : 316 – 326 .
  • S. K. Suneja , C. S. Lalitha , and S. Khurana ( 2003 ). Second order symmetric duality in multiobjective programming . European J. Oper. Res. 144 : 492 – 500 .
  • S. K. Suneja , M. K. Srivastava , and M. Bhatia ( 2008 ). Higher order duality in multiobjective fractional programming with support functions . J. Math. Anal. Appl. 347 : 8 – 17 .
  • M. N. Vartak and I. Gupta ( 1987 ). Duality theory for fractional programming problems under η-convexity . Opsearch 24 : 163 – 174 .
  • X. M. Yang ( 1995 ). Second order symmetric duality for nonlinear programs . Opsearch 32 : 205 – 209 .
  • X. M. Yang ( 2009 ). On second order symmetric duality in nondifferentiable multiobjective programming . J. Ind. Manag. Optim. 5 : 697 – 703 .
  • X. M. Yang and S. H. Hou ( 2001 ). Second-order symmetric duality in multiobjective programming . Appl. Math. Lett. 14 : 587 – 592 .
  • X. M. Yang , K. L. Teo , and X. Q. Yang ( 2004 ). Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming . J. Math. Anal. Appl. 297 : 48 – 55 .
  • X. M. Yang , X. Q. Yang , and K. L. Teo ( 2003 ). Nondifferentiable second order symmetric duality in mathematical programming with F-convexity . European J. Oper. Res. 144 : 554 – 559 .
  • X. M. Yang , X. Q. Yang , and K. L. Teo ( 2005 ). Huard type second-order converse duality for nonlinear programming . Appl. Math. Lett. 18 : 205 – 208 .
  • X. Yang , X. Q. Yang , and K. L. Teo ( 2008 ). Higher-order symmetric duality in multiobjective programming with invexity . J. Ind. Manag. Optim. 4 : 385 – 391 .
  • X. M. Yang , X. Q. Yang , K. L. Teo , and S. H. Hou ( 2004 ). Second order duality for nonlinear programming . Indian J. Pure Appl. Math. 35 : 699 – 708 .
  • X. M. Yang , X. Q. Yang , K. L. Teo , and S. H. Hou ( 2005 ). Multiobjective second-order symmetric duality with F-convexity . European J. Oper. Res. 165 : 585 – 591 .
  • X. M. Yang and P. Zhang ( 2005 ). On second-order converse duality for a nondifferentiable programming problem . Bull. Austral. Math. Soc. 72 : 265 – 270 .
  • X. Q. Yang ( 1998 ). Second-order global optimality conditions for convex composite optimization . Math. Prog. 81 : 327 – 347 .
  • G. J. Zalmai ( 1989 ). Optimality conditions and duality for constrained measurable subset selection problems with minmax objective functions . Optimization 2 : 377 – 395 .
  • G. J. Zalmai and Q. Zhang ( 2007 ). Global nonparametric sufficient optimality conditions for semi-infinite discrete minmax fractional programming problems involving generalized (η, ρ)-invex functions . Numer. Funct. Anal. Optim. 28 : 173 – 209 .
  • G. J. Zalmai and Q. Zhang ( 2007 ). Nonparametric duality models for semi-infinite discrete minmax fractional programming problems involving generalized (η, ρ)-invex functions . Numer. Funct. Anal. Optim. 28 : 211 – 243 .
  • J. Zhang and B. Mond ( 1996 ). Second order b-invexity and duality in mathematical programming . Utilitas Math. 50 : 19 – 31 .
  • J. Zhang and B. Mond ( 1997 ). Second order duality for multiobjective nonlinear programming involving generalized convexity . In Proceedings of the Optimization Miniconference III ( B. M. Glover , B. D. Craven , and D. Ralph , Eds.). University of Ballarat , Victoria , Australia , pp. 79 – 95 .

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