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Sufficiency and duality in multiobjective programming involving generalized \((F,\rho)\)-convexity. (English) Zbl 0973.90069
Summary: New classes of generalized \((F,\rho)\)-convexity are introduced for vector-valued functions. Examples are given to show their relations with \((F,\rho)\)-pseudoconvex, \((F,\rho)\)-quasiconvex, and strictly \((F,\rho)\)-pseudoconvex vector-valued functions. The sufficient optimality conditions and duality results are obtained for multiobjective programming involving generalized \((F,\rho)\)-convex vector-valued functions.

MSC:
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
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