Geodesic
Convergence results for a class of abstract continuous descent methods
Electronic journal of differential equations, Tome 2004 (2004)
We study continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish convergence theorems for those methods which are generated by approximate solutions to evolution equations governed by regular vector fields. Since the complement of the set of regular vector fields is $\sigma$-porous, we conclude that our results apply to most vector fields in the sense of Baire's categories.
Classification : 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25
Keywords: complete metric space, descent method, Lipschitzian function, porous set, regular vector field 
@article{EJDE_2004__2004__a46,
     author = {Aizicovici,  Sergiu and Reich,  Simeon and Zaslavski,  Alexander J.},
     title = {Convergence results for a class of abstract continuous descent methods},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1062.90065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a46/}
}
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AU  - Zaslavski,  Alexander J.
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%A Zaslavski,  Alexander J.
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%J Electronic journal of differential equations
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%F EJDE_2004__2004__a46
Aizicovici,  Sergiu; Reich,  Simeon; Zaslavski,  Alexander J. Convergence results for a class of abstract continuous descent methods. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a46/