Point-based set-valued approximation, C-differentiable operator and application
Point-based set-valued approximation, C-differentiable operator and application
In this article, we investigate the point-based set-valued approximation [H. Xu (1999). Set-valued approximation and Newton's methods. Mathematical Programming, 84, 401-420.] and the C-differential operator [L. Qi (1996). C-Differential operators, C-differentiability and generalized Newton methods, Applied Mathematics Report, AMR96/5, School of Mathematics, The University of New South Wales, Sydney, Australia.] of a vector valued function. Several questions about C-differential operators posed in [L. Qi (1996). C-Differential operators, C-differentiability and generalized Newton methods, Applied Mathematics Report, AMR96/5, School of Mathematics, The University of New South Wales, Sydney, Australia.] are answered. Further, we discuss the application of C-differential operator in nonsmooth optimization. We derive optimality conditions and establish a mean value theorem in terms of convex C-differential operators. Finally, we propose a conceptual algorithm based on the convex C-differential operators.
point-based set-valued approximation, convex C-differential operator, plenary hull, mean value theorem
127-143
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
2003
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Xu, Huifu
(2003)
Point-based set-valued approximation, C-differentiable operator and application.
Optimization, 52 (2), .
(doi:10.1080/0233193021000058922).
Abstract
In this article, we investigate the point-based set-valued approximation [H. Xu (1999). Set-valued approximation and Newton's methods. Mathematical Programming, 84, 401-420.] and the C-differential operator [L. Qi (1996). C-Differential operators, C-differentiability and generalized Newton methods, Applied Mathematics Report, AMR96/5, School of Mathematics, The University of New South Wales, Sydney, Australia.] of a vector valued function. Several questions about C-differential operators posed in [L. Qi (1996). C-Differential operators, C-differentiability and generalized Newton methods, Applied Mathematics Report, AMR96/5, School of Mathematics, The University of New South Wales, Sydney, Australia.] are answered. Further, we discuss the application of C-differential operator in nonsmooth optimization. We derive optimality conditions and establish a mean value theorem in terms of convex C-differential operators. Finally, we propose a conceptual algorithm based on the convex C-differential operators.
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Published date: 2003
Keywords:
point-based set-valued approximation, convex C-differential operator, plenary hull, mean value theorem
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Operational Research
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Local EPrints ID: 29695
URI: http://eprints.soton.ac.uk/id/eprint/29695
ISSN: 0233-1934
PURE UUID: f447ac73-e25e-4aa8-bfd2-6731d4c47479
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 03:31
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Author:
Huifu Xu
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