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Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces. (English) Zbl 1095.90105
The authors generalize the definition of preinvexity to mappings taking values in a Banach space. They prove a Gordan type alternative theorem for such functions and use it to derive necessary optimality conditions for scalar optimization problems with preinvex objective and constraint functions. These conditions are then extended to vector optimization problems by means of a scalarization result for weakly efficient points of preinvex mappings. Sufficient optimality conditions for such preinvex vector optimization problems are also obtained. Finally, the authors prove that local weakly efficient points of preinvex mappings are necessarily global weakly efficient.
MSC:
90C29Multi-objective programming; goal programming
26B25Convexity and generalizations (several real variables)
90C46Optimality conditions, duality