Implicit Smoothing and Its Application to Optimization with Piecewise Smooth Equality Constraints1

D. Ralph and H. Xu
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D. Ralph: University of Cambridge
H. Xu: University of Southampton

Journal of Optimization Theory and Applications, 2005, vol. 124, issue 3, No 8, 673-699

Abstract: Abstract In this paper, we discuss the smoothing of an implicit function defined by a nonsmooth underdetermined system of equations F(y,z) = 0. We apply a class of parametrized smoothing methods to smooth F and investigate the limiting behavior of the implicit function solving the smoothed equations. In particular, we discuss the approximation of the Clarke generalized Jacobian of the implicit function when F is piecewise smooth. As an application, we present an analysis of the generalized Karush-Kuhn-Tucker conditions of different forms for a piecewise-smooth equality-constrained minimization problem.

Keywords: Clarke generalized Jacobian; B-subdifferential; smoothing Jacobians; generalized Karush-Kuhn-Tucker conditions; piecewise smooth functions; strong Jacobian consistency; index-consistent functions; essentially index consistent functions; essentially active indices (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-004-1180-1

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