Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization
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Date
2020
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Journal ISSN
Volume Title
Publisher
Universal Wiser Publisher
Abstract
Let X, Y be Hilbert spaces and F: X ? Y be Fréchet differentiable. Suppose that F? is center-Lipschitz on U(w, r) and F?(w) be a surjection. Then, S<inf>1</inf> = F(U(w, ?<inf>1</inf>)) is convex where ?<inf>1</inf> ? r. The set S<inf>1</inf> contains the corresponding set given in [18] under the Lipschitz condition. Numerical examples where the old conditions are not satisfied but the new conditions are satisfied are provided in this paper. © 2020 Ioannis K. Argyros, et al. DOI: https://doi.o.
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Keywords
control theory, convexity, image of a ball, Newton’s method, optimization
Citation
Contemporary Mathematics (Singapore), 2020, 1, 4, pp. 209-214