Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization

Ioannis K. Argyros; Yeol Je Cho; Santhosh George

doi:10.37256/cm.142020405

Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization

Authors

Ioannis K. Argyros Department of Mathematicsal Sciences, Cameron University, Lawton, OK 73505, USA
Yeol Je Cho School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P. R. China, and Department of Mathematics Education, Gyeongsang National University Jinju 52828, Korea
Santhosh George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka 757025, India

DOI:

https://doi.org/10.37256/cm.142020405

Keywords:

convexity, Newton's method, optimization, control theory, image of a ball

Abstract

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.

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Published

2020-08-20

How to Cite

Ioannis K. Argyros, Yeol Je Cho, Santhosh George. Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization. Contemp. Math. [Internet]. 2020 Aug. 20 [cited 2024 Apr. 27];1(4):209-14. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/405

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Issue

Contemporary Mathematics, Volume 1 Issue 4 (2020), 170-271

Section

Research Article

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization

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