On the duality in convex vector optimization. (Sur la dualité en optimisation vectorielle convexe.) (French) Zbl 0830.90123

Summary: We consider a fairly general minimization problem in convex vector optimization. We define and study its dual and obtain as special cases, many existing results on the matter. Isermann’s main duality result in the linear case will be improved. For working tools, we generalize several results used in convex scalar optimization to the vector case. On the way, we show that a result on duality and alternative in multiobjective optimization needs not satisfy the hypothesis of the domination property to hold.


90C29 Multi-objective and goal programming
90C25 Convex programming
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