Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. Such a strengthening is required in order to obtain genericity results.

Keywords:

differentiability, generic, marginal, performance function, subdifferential differentiability, generic, marginal, performance function, subdifferential

MSC Classifications:

26B05, 65K10, 54C60, 90C26, 90C48 show english descriptions Continuity and differentiation questions
Optimization and variational techniques [See also 49Mxx, 93B40]
Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
Nonconvex programming, global optimization
Programming in abstract spaces 26B05 - Continuity and differentiation questions
65K10 - Optimization and variational techniques [See also 49Mxx, 93B40]
54C60 - Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
90C26 - Nonconvex programming, global optimization
90C48 - Programming in abstract spaces

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