Higher Order Fractional Symmetric Duality Over Cone Constraints

In this paper, a pair of Mond-Weir type higher order fractional symmetric dual program over cone constraints is formulated. Under higher order invexity assumptions, we prove weak, strong and strict duality theorems. Moreover, a self dual program is formulated and self duality theorem is discussed.

[1]  T. R. Gulati,et al.  Symmetric duality for second-order fractional programs , 2013, Optim. Lett..

[2]  Suresh Chandra,et al.  Symmetric dual fractional programming , 1985, Z. Oper. Research.

[3]  R. Agarwal,et al.  Generalized Second-Order Mixed Symmetric Duality in Nondifferentiable Mathematical Programming , 2011 .

[4]  Izhar Ahmad,et al.  Second order symmetric duality in nondifferentiable multiobjective programming , 2005, Inf. Sci..

[5]  Mohamed Abd El-Hady Kassem,et al.  Higher-order symmetric duality in vector optimization problem involving generalized cone-invex functions , 2009, Appl. Math. Comput..

[6]  Olvi L. Mangasarian,et al.  Second- and higher-order duality in nonlinear programming☆ , 1975 .

[7]  Xinmin Yang On symmetric and self duality in vector optimization problem , 2011 .

[8]  S. K. Gupta,et al.  Higher-order symmetric duality with cone constraints , 2009, Appl. Math. Lett..

[9]  Seema Khurana,et al.  Symmetric duality in multiobjective programming involving generalized cone-invex functions , 2005, Eur. J. Oper. Res..

[10]  G. Dantzig,et al.  Symmetric dual nonlinear programs. , 1965 .

[11]  Mokhtar S. Bazaraa,et al.  On Symmetric Duality in Nonlinear Programming , 1973, Oper. Res..

[12]  W. Ziemba,et al.  Generalized concavity in optimization and economics , 1981 .

[13]  Mohamed Abd El-Hady Kassem,et al.  Symmetric and self duality in vector optimization problem , 2006, Appl. Math. Comput..

[14]  Izhar Ahmad,et al.  Secound Order Symmetric Duality with Generalized Convexity , 2001 .

[15]  Xiuhong Chen,et al.  Higher-order symmetric duality in nondifferentiable multiobjective programming problems , 2004 .

[16]  Izhar Ahmad,et al.  A note on higher-order nondifferentiable symmetric duality in multiobjective programming , 2011, Appl. Math. Lett..

[17]  C Tofallis,et al.  Fractional Programming: Theory, Methods and Applications , 1997, J. Oper. Res. Soc..

[18]  Izhar Ahmad,et al.  Second-order symmetric duality with cone constraints , 2008 .

[19]  I. M. Stancu-Minasian,et al.  A sixth bibliography of fractional programming , 2006 .

[20]  Suresh Chandra,et al.  A note on pseudo-invexity and symmetric duality , 1998, Eur. J. Oper. Res..

[21]  Izhar Ahmad,et al.  Second order symmetric duality for nonlinear minimax mixed integer programs , 1997 .