Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization
Let X, Y be Hilbert spaces and F : X → Y be Frechet differentiable. Suppose that F′ is center-Lipschitz on U(w, r) and F′(w) be a surjection. Then, S1 = F(U(w, ε1)) is convex where ε1 ≤ r. The set S1 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.
2008 ◽
Vol 118
(5)
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pp. 818-838
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2008 ◽
Vol 8
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pp. 237-252
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2009 ◽
Vol 14
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pp. 187-198
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2021 ◽
Vol 0
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