Optimality and duality for \(E\)-differentiable multiobjective programming problems involving \(E\)-type I functions. (English) Zbl 1524.90275
Summary: In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable multiobjective programming problems with \(E\)-differentiable functions. Namely, the concept of \(E\)-type I functions is defined for \(E\)-differentiable multiobjective programming problem. Based on the introduced concept of generalized convexity, the sufficiency of the so-called \(E\)-Karush-Kuhn-Tucker optimality conditions are established for a feasible point to be an \(E\)-efficient or a weakly \(E\)-efficient solution. Further, the so-called vector Mond-Weir \(E\)-dual problem is defined for the considered \(E\)-differentiable multiobjective programming problem and several \(E\)-duality theorems in the sense of Mond-Weir are derived under appropriate generalized \(E\)-type I functions.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C26 | Nonconvex programming, global optimization |
| 90C30 | Nonlinear programming |
| 26B25 | Convexity of real functions of several variables, generalizations |
Keywords:
\(E\)-type I functions; generalized convexity; \(E\)-differentiable function; \(E\)-optimality conditions; \(E\)-Mond-Weir dualityReferences:
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