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Relation between Demyanov difference and Minkowski difference of convex compact subsets in \(R^2\). (English) Zbl 1111.49010

Summary: A necessary and sufficient condition for Demyanov difference and Minkowski difference of compact convex subsets in \(R^2\) being equal is given in this paper. Several examples are computed by Matlab to test our result. The necessary and sufficient condition makes us to compute Clarke subdifferential by quasidifferential for a special of Lipschitz functions.

MSC:

49J52 Nonsmooth analysis
90C26 Nonconvex programming, global optimization
49N15 Duality theory (optimization)

Software:

Matlab
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Full Text: DOI

References:

[1] V. F. Demyanov,On a relation between the Clarke subdifferential and quasidifferential, Vestnik Leninggrad University13 (1981), 183–189. · Zbl 0473.49008
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[6] Y. Gao,Representative of quasidifferentials and its formula for a quasidifferentiable func tion, Set-Valued Analysis13 (2005), 323–336. · Zbl 1086.49017 · doi:10.1007/s11228-005-4403-1
[7] A. M. Rubinov and I. S. Akhundov,Difference of compact convex sets in the sense of Demyanov and its applications in nonsmooth analysis, Optimization23 (1992), 179–188. · Zbl 0816.52002 · doi:10.1080/02331939208843757
[8] A. M. Rubinov,Difference of convex compact sets and their application in nonsmooth analysis, Nonsmooth Optimization Methods and Applications, Singapore, 1991, 366–378. · Zbl 1050.49514
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