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Sensitivity analysis of composite piecewise smooth equations

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Abstract

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 typef=g °h whereg is piecewise smooth andh is smooth and present verifiable conditions which ensure that the functionf=g °\(\tilde h\) is a Lipschitzian homeomorphism near a given point for every\(\tilde h\) sufficiently close toh with respect to theC 1-topology.

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Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, 3052, Parkville, Vic., Australia

    Daniel Ralph

  2. Department of Engineering, University of Cambridge, CB2 1PZ, Cambridge, England

    Stefan Scholtes

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  1. Daniel Ralph
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  2. Stefan Scholtes
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Additional information

Revised version of part of the paper “Sensitivity analysis and Newton’s method for composite piecewise smooth equations”.

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Ralph, D., Scholtes, S. Sensitivity analysis of composite piecewise smooth equations. Mathematical Programming 76, 593–612 (1997). https://doi.org/10.1007/BF02614400

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  • DOI: https://doi.org/10.1007/BF02614400

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