Abstract
For E a metric space, f:E→ℝ.Ø≠C ⊂ E closed, we consider the value function μ(f,C) = inf{f(c): c ∈ C. One studies the continuity of ?(f,.) by using a family of set convergences recently introduced. “Conversely”, one obtains results concerning these convergences, proving a posteriori the interest of the principle of classification of convergences proposed by Sonntag and Zalinescu (1991a), (1991b).
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References
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© 1992 Springer Basel AG
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Sonntag, Y. (1992). Continuity of the value function with respect to the set of constraints. In: Barbu, V., Tiba, D., Bonnans, J.F. (eds) Optimization, Optimal Control and Partial Differential Equations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 107. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8625-3_29
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DOI: https://doi.org/10.1007/978-3-0348-8625-3_29
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9704-4
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