Programming problems involving generalized convex set functions. (English) Zbl 0984.90047
Takahashi, Wataru (ed.) et al., Nonlinear analysis and convex analysis. Proceedings of the 1st international conference (NACA98), Niigata, Japan, July 28-31, 1998. Singapore: World Scientific. 34-43 (1999).
Summary: For an atomless finite measure space \((X,\Gamma,\mu)\) with \(L^1(X,\Gamma,\mu)\) separable, we study a fractional programming problem involving generalized convex set functions defined over a convex family \({\mathcal S}\) of measurable subsets in the \(\sigma\)-algebra \(\Gamma\). We establish some necessary and sufficient optimality conditions for such programming problems.
For the entire collection see [Zbl 0969.00060].
For the entire collection see [Zbl 0969.00060].
MSC:
| 90C32 | Fractional programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 52A41 | Convex functions and convex programs in convex geometry |
| 28B99 | Set functions, measures and integrals with values in abstract spaces |
