Duality for second-order symmetric multiobjective programming with cone constraints

In this paper, a new pair of Mond-Weir type multiobjective second-order symmetric dual models with cone constraints is formulated in which the objective function is optimised with respect to an arbitrary closed convex cone. Usual duality relations are further established under K-η -bonvexity/second-order symmetric dual K-H -convexity assumptions. A nontrivial example has also been illustrated to justify the weak duality theorems. Several results including many recent works are obtained as special cases.

[1]  Sudha Gupta,et al.  Duality in multiobjective nonlinear programming involving semilocally convex and related functions , 1998, Eur. J. Oper. Res..

[2]  Geeta,et al.  Nondifferentiable multiobjective symmetric dual programs over cones , 2011 .

[3]  T. R. Gulati,et al.  Nondifferentiable multiobjective Mond–Weir type second-order symmetric duality over cones , 2010, Optim. Lett..

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

[5]  Santanu K. Mishra,et al.  Multiobjective second order symmetric duality with cone constraints , 2000, Eur. J. Oper. Res..

[6]  Yu Jung Lee,et al.  Nondifferentiable higher order duality in multiobjective programming involving cones , 2009 .

[7]  S. Sinha.  A Duality Theorem for Nonlinear Programming , 1966 .

[8]  S. K. Gupta,et al.  Second-order multiobjective symmetric duality with cone constraints , 2010, Eur. J. Oper. Res..

[9]  Kok Lay Teo,et al.  Second order symmetric duality in non-differentiable multiobjective programming with F , 2005, Eur. J. Oper. Res..

[10]  Aquil Ahmed,et al.  Multiobjective symmetric duality with invexity , 1997, Bulletin of the Australian Mathematical Society.

[11]  Do Sang Kim,et al.  Second-order symmetric and self duality in multiobjective programming☆ , 1997 .

[12]  Houduo Qi,et al.  Local Duality of Nonlinear Semidefinite Programming , 2009, Math. Oper. Res..

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

[14]  I. Ahmad.  MULTIOBJECTIVE MIXED SYMMETRIC DUALITY WITH INVEXITY , 2005 .

[15]  Joseph C. Paradi,et al.  Developing a mathematical programming model for sensitivity analysis in analytic hierarchy process , 2010, Int. J. Math. Oper. Res..

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

[17]  Laura Palagi,et al.  Convergence to Second-Order Stationary Points of a Primal-Dual Algorithm Model for Nonlinear Programming , 2005, Math. Oper. Res..

[18]  Boris S. Mordukhovich,et al.  Variational Analysis in Nonsmooth Optimization and Discrete Optimal Control , 2007, Math. Oper. Res..

[19]  C. R. Bector,et al.  On Mixed Symmetric Duality in Multiobjective Programming , 1999 .

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

[22]  T. R. Gulati,et al.  Nondifferentiable multiobjective symmetric duality with F -convexity over cones , 2011 .

[23]  Immanuel M. Bomze,et al.  A Conic Duality Frank-Wolfe-Type Theorem via Exact Penalization in Quadratic Optimization , 2009, Math. Oper. Res..

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

[25]  Kok Lay Teo,et al.  Second-order duality for nonlinear programming , 2004 .

[26]  Vasile Preda,et al.  On a general duality model in multiobjective fractional programming with n-set functions , 2011, Math. Comput. Model..

[27]  Do Sang Kim,et al.  Non-differentiable symmetric duality for multiobjective programming with cone constraints , 2008, Eur. J. Oper. Res..

[28]  Jiang Wang,et al.  Evaluating Portfolio Policies: A Duality Approach , 2003, Oper. Res..

[29]  C. S. Lalitha,et al.  Second order symmetric duality in multiobjective programming , 2003, Eur. J. Oper. Res..

[30]  S. K. Gupta,et al.  Nondifferentiable multiobjective second-order symmetric duality , 2011, Optim. Lett..

[31]  S. K. Gupta,et al.  Wolfe type second-order symmetric duality in nondifferentiable programming , 2005 .

[32]  Izhar Ahmad,et al.  Second-order duality in nondifferentiable fractional programming , 2011 .

[33]  Izhar Ahmad,et al.  Nondifferentiable second order symmetric duality in multiobjective programming , 2005, Appl. Math. Lett..

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

[35]  Xiaoqi Yang,et al.  Lagrange Multipliers in Nonsmooth Semi-Infinite Optimization Problems , 2007, Math. Oper. Res..

[36]  Panagiotis Xidonas,et al.  A multicriteria decision making approach for the evaluation of equity portfolios , 2010, Int. J. Math. Oper. Res..

[37]  T. R. Gulati,et al.  Mond-Weir type second-order symmetric duality in multiobjective programming over cones , 2010, Appl. Math. Lett..

[38]  A Strict Converse Duality Theorem in Nonlinear Programming , 1983 .

[39]  Mark W. Lewis,et al.  Computationally attractive non-linear models for combinatorial optimisation , 2009, Int. J. Math. Oper. Res..

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

[42]  B. Mond.  A Class of Nondifferentiable Fractional Programming Problems , 1978 .

[43]  Defeng Sun,et al.  Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming , 2008, SIAM J. Optim..

[44]  Anurag Jayswal,et al.  Multiobjective higher-order symmetric duality involving generalized cone-invex functions , 2010, Comput. Math. Appl..

[45]  On Strict Converse Duality In Nonlinear Programming , 1985 .

[46]  Bertram Mond,et al.  Duality with generalized convexity , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[47]  Surjeet Kaur Suneja,et al.  Multiobjective symmetric duality involving cones , 2002, Eur. J. Oper. Res..

[48]  T. R. Gulati,et al.  On some symmetric dual models in multiobjective programming , 2009, Appl. Math. Comput..

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

[50]  M. A. Hanson,et al.  Further Generalizations of Convexity in Mathematical Programming , 1982 .

[51]  Izhar Ahmad,et al.  Multiobjective mixed symmetric duality involving cones , 2010, Comput. Math. Appl..