Lagrangian duality for preinvex set-valued functions. (English) Zbl 0894.90142
Summary: Generalizing the concept of cone convexity, we have defined cone preinvexity for set-valued functions and given an example in support of this generalization. A Farkas-Minkowski type theorem has been proved for these functions. A Lagrangian type dual has been defined for a fractional programming problem involving preinvex set-valued functions and duality results are established.
MSC:
| 90C32 | Fractional programming |
| 26B25 | Convexity of real functions of several variables, generalizations |
| 90C48 | Programming in abstract spaces |
| 54C60 | Set-valued maps in general topology |
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