Implicit smoothing and its application to optimization with piecewise smooth equality constraints
Implicit smoothing and its application to optimization with piecewise smooth equality constraints
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.
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
673-699
Ralph, D.
eeaa534f-e6ab-4cf6-a915-ff0da511d583
Xu, H.
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
2005
Ralph, D.
eeaa534f-e6ab-4cf6-a915-ff0da511d583
Xu, H.
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ralph, D. and Xu, H.
(2005)
Implicit smoothing and its application to optimization with piecewise smooth equality constraints.
Journal of Optimization Theory and Applications, 124 (3), .
(doi:10.1007/s10957-004-1180-1).
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.
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Published date: 2005
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
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Operational Research
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Local EPrints ID: 29662
URI: http://eprints.soton.ac.uk/id/eprint/29662
ISSN: 0022-3239
PURE UUID: 65acefae-6d4d-4067-948c-96c065dc3d4e
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 03:31
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Author:
D. Ralph
Author:
H. Xu
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