×

zbMATH — the first resource for mathematics

Stability in mathematical programming with nondifferentiable data. (English) Zbl 0538.49020
Let W be an open set in \(R^ q\) and let \(f_ i\), \(g_ j (i=0,...,m\); \(j=1,...,p)\) be real-valued Lipschitzian functions defined on \(R^ N\times W\). The following problem is considered: minimize \(f_ 0(x,w)\) subject to \(f_ i(x,w)\leq 0 (i=1,...,m)\), \(g_ j(x,w)=0 (j=1,...,p)\), \(x\in R^ N\), 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.
Reviewer: M.Hanson

MSC:
49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization
26B05 Continuity and differentiation questions
28A15 Abstract differentiation theory, differentiation of set functions
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
49K10 Optimality conditions for free problems in two or more independent variables
90C30 Nonlinear programming
26A16 Lipschitz (Hölder) classes
PDF BibTeX XML Cite
Full Text: DOI