Second order symmetric duality in mathematical programming with F-convexity

Nondifferentiable Second-Order Minimax Mixed Integer Symmetric Duality

“…(iv) If we take C = {0} and D = {0}, then our programs reduce to the problem (NP) and (ND) studied in Mishra [11].…”

Higher-order symmetric duality for a class of multiobjective fractional programming problems

“…For a differentiable function h: R n ×R n R, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second order F-convexity in [15] and higher-order F -convexity in [14]. Under the higher-order (F, a, r, d)-convexity assumptions, we prove the higherorder weak, higher-order strong and higher-order converse duality theorems.…”

Second Order Mixed Symmetric Duality in Non-Differentiable Multi-Objective Mathematical Programming

“…The symmetric duality for scalar programming has been studied extensively in the literature, one can refer to Dantzig et al [5], Mishra [14]- [16], Mond [18], Mond and Weir [21].…”

“…Mond [19] was the first one to present second order symmetric dual models and proved second order symmetric duality theorems under convexity assumptions. Mishra [15] established Wolfe type and Mond-Weir type second order symmetric duality for nonlinear programming problems under second order generalized convexity assumptions. Hou and Yang [11] and Yang et al [26] extended the results of Mishra [15] to the non-differentiable case.…”

“…Mishra [15] established Wolfe type and Mond-Weir type second order symmetric duality for nonlinear programming problems under second order generalized convexity assumptions. Hou and Yang [11] and Yang et al [26] extended the results of Mishra [15] to the non-differentiable case. Suneja et al [24] extended the results of Mishra [15] to the multiobjective case.…”