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Sensitivity analysis of composite piecewise smooth equations. (English) Zbl 0871.90094

Summary: This paper is a contribution to the sensitivity analysis of piecewise smooth equations. A piecewise smooth function is a Lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible \(B\)-derivative at this point. We emphasise the role of functions of the type \(f=g\circ h\) where \(g\) is piecewise smooth and \(h\) is smooth and present verifiable conditions which ensure that the function \(f=g\circ \widetilde{h}\) is a Lipschitzian homeomorphism near a given point for every \(\widetilde{h}\) sufficiently close to \(h\) with respect to the \(C^1\)-topology.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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