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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

90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming
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