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.

References

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Published

2020-08-20

Issue

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

Section

Research Article

License

Copyright (c) 2020 Ioannis K. Argyros, Yeol Je Cho, Santhosh George

Creative Commons License

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

How to Cite

1.
Extending the Convexity of Nonlinear Image of a Ball Appearing in Optimization. Contemp. Math. [Internet]. 2020 Aug. 20 [cited 2025 Dec. 24];1(4):209-14. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/405