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Kouada, Issoufou

Upper-semi-continuity and cone-concavity of multi-valued vector functions in a duality theory for vector optimization. (English) Zbl 0889.90132

Math. Methods Oper. Res. 46, No. 2, 169-192 (1997).
Summary: Following a few words on multifunctions in the mathematical literature, a very brief recall on dual spaces, some preliminary notations and definitions in the introduction, we give some results on those functions in the second paragraph. In the third paragraph, a duality theory in cone-optimization involving multifunctions is developed with the concept of the strong instead of the weak cone-optimality criterium. The results so obtained account for existing ones on univocal vector-function optimization and they hold in spaces of arbitrary dimension.

Cited in 2 Documents

MSC:

90C30 Nonlinear programming
54C60 Set-valued maps in general topology
49J52 Nonsmooth analysis
90C29 Multi-objective and goal programming
90C48 Programming in abstract spaces

Keywords:

multifunction; semi-continuity; convexity; cone-concavity; recession cone; primal problem; dual problem; cone-maximal solution
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\textit{I. Kouada}, Math. Methods Oper. Res. 46, No. 2, 169--192 (1997; Zbl 0889.90132)
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