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In this paper, we study a class of nonsmooth multiobjective optimization problem including inequality constraints. To the aim, some new functions named (pseudo, quasi) invex of order $\sigma(B, \varphi)-V-$ type II and strongly (quasi, pseudo) invex of order $\sigma(B, \varphi)-V-$ type II are introduced by using the tools of Clarke subdifferential. These new functions are used to derive and prove the sufficient optimality condition for a strict minimizer of the multiobjective programming problems. Moreover, the corresponding duality theorems are formulated for general Mond-Weir type dual program.
optimality condition, duality, multiobje-ctive optimization problem
This work is supported by Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 15JK1456); Natural Science Foundation of shaanxi Province of China (Program No. 2017JM1041).
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