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On generalized semicontinuity-preserving multifunctions. (English) Zbl 0613.90083
The parametric mathematical programming problem of finding an optimal y for the objective function $$f: X\times Y\to {\mathbb{R}}$$ subject to the restriction $$y\in F(x)$$ (with $$F: X\to Y$$ a given multifunction) is considered and the continuity of its optimal value $$v(x)=\sup \{f(x,y)$$; $$y\in F(x)\}$$ is studied. For this purpose a generalized concept of ”semicontinuity” for multifunctions is introduced and used for giving ”stability criteria” for v.
Reviewer: D.Butnariu

##### MSC:
 90C31 Sensitivity, stability, parametric optimization 90C30 Nonlinear programming
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##### References:
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