Motivated by important applications, the theory of mathematical programming has been extended to the case of infinitely many restrictions. At the same time, this theory knew remarcable developments since invexity and its further generalizations have been introduced as substitute of convexity. Here, we consider the multiobjective programming with a set of restrictions indexed in a compact. We obtain optimality criteria of Kuhn-Tucker type under new weaker invexity conditions. Also some dual probles are introduced and it is proved that the weak and strong duality properties hold within the same environement.
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