On the Calculus of Limiting Subjets on Riemannian Manifolds
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In this paper fuzzy calculus rules for subjets of order two on finite dimensional Riemannian manifolds are obtained. Then a second order singular subjet derived from a sequence of efficient subsets of symmetric matrices is introduced. Employing fuzzy calculus rules for subjets of order two and various qualification assumptions based on a second order singular subjet, calculus rules for limiting subjets on a finite dimensional Riemannian manifold are obtianed.
Mathematics Subject Classification (2010)Primary 49J52 Secondary 58C20
KeywordsSubhessians Subjets Second order subdifferential calculus Riemannian manifolds
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- 6.F. H. Clarke, Yu. S. Ledayaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory. Grad. Texts in Math. 178, Springer, 1998.Google Scholar
- 8.M. G. Crandall, Viscosity solutions: a primer. Viscosity solutions and applications, 1-43, Lecture Notes in Math. 1660, Springer, 1997.Google Scholar
- 11.A. Eberhard, Prox-regularity and subjets. Optimization and Related Topics, 237-313, Appl. Optim. 47 Kluwer Academic Publ. 2001.Google Scholar
- 15.C. Li, B. S. Mordukhovich, J. Wang and J. C. Yao, Weak sharp minima on Riemannian manifolds. to appear in SIAM J. Optim.Google Scholar
- 16.T. Sakai, Riemannian Geometry, Trans. Math. Monogr. 149, Amer. Math. Soc. 1992.Google Scholar