Auslender, Alfred Stability in mathematical programming with nondifferentiable data. (English) Zbl 0538.49020 SIAM J. Control Optimization 22, 239-254 (1984). 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 Cited in 4 ReviewsCited in 99 Documents 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 Keywords:second-order directional derivative; locally Lipschitzian functions; isolated minimizers PDFBibTeX XMLCite \textit{A. Auslender}, SIAM J. Control Optim. 22, 239--254 (1984; Zbl 0538.49020) Full Text: DOI