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Zbl 0538.49020
Auslender, Alfred
Stability in mathematical programming with nondifferentiable data.
(English)
[J] SIAM J. Control Optimization 22, 239-254 (1984). ISSN 0363-0129; ISSN 1095-7138/e

Let W be an open set in $R\sp q$ and let $f\sb i$, $g\sb j (i=0,...,m$; $j=1,...,p)$ be real-valued Lipschitzian functions defined on $R\sp N\times W$. The following problem is considered: minimize $f\sb 0(x,w)$ subject to $f\sb i(x,w)\le 0 (i=1,...,m)$, $g\sb j(x,w)=0 (j=1,...,p)$, $x\in R\sp N$, where the parameter w belongs to a neighborhood of point $\bar w\in W$. Conditions for $\bar x$ to be an isolated local minimum are given, and bounds are found for the variations of some classes of isolated minimizers.
[M.Hanson]
MSC 2000:
*49K40 Sensitivity of optimal solutions in the presence of perturbations
90C31 Sensitivity, etc.
26B05 Continuity and differentiation questions (several real variables)
28A15 Differentiation of set functions
26A24 Differentiation of functions of one real variable
49K10 Free problems in several independent variables (nec./ suff.)
90C30 Nonlinear programming
26A16 Lipschitz classes, etc. (one real variable)

Keywords: second-order directional derivative; locally Lipschitzian functions; isolated minimizers

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