First several new classes of higher order (φ, η, ω, π, ρ, θ, m)-invexities are introduced, and then a set of higher-order parametric necessary optimality conditions and several sets of higher order sufficient optimality conditions for a discrete minmax fractional programming problem applying various higher order (φ, η, ω, π, ρ, θ, m)-invexity constraints are established. The obtained results are new and generalize a wide range of results in the literature.
Chinchuluun A, Pardalos PM. A survey of recent developments in multiobjective optimization. Annals of Operations Research 2007; 154: 29-50. http://dx.doi.org/10.1007/s10479-007-0186-0
Pitea A, Postolache M. Duality theorems for a new class of multitime multiobjective variational problems. Journal of Global Optimization 2012; 54(1): 47-58. http://dx.doi.org/10.1007/s10898-011-9740-z
Pitea A, Postolache M. Minimization of vectors of curvilinear functionals on the second order jet bundle: Necessary conditions. Optimization Letters 2012; 6(3): 459-70. http://dx.doi.org/10.1007/s11590-010-0272-0
Pitea A, Postolache M. Minimization of vectors of curvilinear functionals on the second order jet bundle: Sufficient efficiency conditions. Optimization Letters 2012; 6(8): 1657-69. http://dx.doi.org/10.1007/s11590-011-0357-4
Srivastava MK, Bhatia M. Symmetric duality for multiobjective programming using second order -convexity. Opsearch 2006; 43: 274-95.
Srivastava KK, Govil MG. Second order duality for multiobjective programming involving -type I functions. Opsearch 2000; 37: 316-26.
Verma RU. Weak efficiency conditions for multiobjective fractional programming. Applied Mathematics and Computation 2013; 219: 6819-927. http://dx.doi.org/10.1016/j.amc.2012.12.087
Verma RU. A generalization to Zalmai type second order univexities and applications to parametric duality models to discrete minimax fractional programming. Advances in Nonlinear Variational Inequalities 2012; 15(2): 113-23.
Verma RU. Second order invexity frameworks and efficiency conditions for multiobjective fractional programming. Theory and Applications of Mathematics & Computer Science 2012; 2(1): 31-47.
Verma RU. Role of second order -invexities and parametric sufficient conditions in semiinfinite minimax fractional programming. Transactions on Mathematical Programming and Applications 2013; 1(2): 13-45.
Verma RU, Zalmai GJ. Generalized second-order parametric optimality conditions in discrete minmax fractional programming. Transactions on Mathematical Programming and Applications 2014; 2(12): 1-20.
Yang XM, Yang XQ, Teo KL, Hou SH. Second order duality for nonlinear programming. Indian J. Pure Appl. Math. 2004; 35: 699-708.
Zalmai GJ. General parametric sufficient optimality conditions for discrete minmax fractional programming problems containing generalized -V-invex functions and arbitrary norms. Journal of Applied Mathematics & Computing 2007; 23(1-2): 1-23. http://dx.doi.org/10.1007/BF02831955
Zalmai GJ. Hanson-Antczak-type generalized invex functions in semiinfinte minmax fractional programming, Part I: Sufficient optimality conditions. Communications on Applied Nonlinear Analysis 2012; 19(4): 1-36.
Zalmai GJ. Hanson - Antczak - type generalized -V- invex functions in semiinfinite multiobjective fractional programming Part I, Sufficient efficiency conditions. Advances in Nonlinear Variational Inequalities 2013; 16(1): 91-114.
Zeidler E. Nonlinear Functional Analysis and its Applications III, Springer-Verlag, New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5020-3
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