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Chou, J. H.; Hsia, Wei-Shen; Lee, Tan-Yu

On multiple objective programming problems with set functions. (English) Zbl 0564.90069

J. Math. Anal. Appl. 105, 383-394 (1985).
The convexity of a subset of a \(\sigma\)-algebra and the convexity of a set function on a convex subset are defined. Related properties are also examined. A Farkas-Minkowski theorem for set functions is then proved. These results are used to characterize properly efficient solutions for multiple objective programming problems with set functions by associated scalar problems.

Cited in 33 Documents

MSC:

90C31 Sensitivity, stability, parametric optimization
26B25 Convexity of real functions of several variables, generalizations

Keywords:

convexity for subsets of sigma-algebras; convexity of set functions; Farkas-Minkowski theorem; efficient solutions; multiple objective programming
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\textit{J. H. Chou} et al., J. Math. Anal. Appl. 105, 383--394 (1985; Zbl 0564.90069)
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References:

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