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Existence and boundedness of solutions to maximal monotone inclusion problem

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Abstract

In Hilbert spaces, the inclusion problem with an arbitrary maximal monotone operator is considered. We prove that the nonemptiness of the solution set of the inclusion problem is equivalent to a coercivity condition. Moreover, a sufficient and necessary condition for the boundedness of the solution set is obtained.

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Acknowledgments

The authors are grateful to the referees for valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, 610066, Sichuan, China

    Yongle Zhang, Yiran He & Yi Jiang

Authors
  1. Yongle Zhang
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  2. Yiran He
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  3. Yi Jiang
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Correspondence to Yongle Zhang.

Additional information

This work is partially supported by National Natural Science Foundation of China (No. 11271274, No. 11126336) and Research Fund of Sichuan Provincial Education Department (No. 14ZB0034).

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Zhang, Y., He, Y. & Jiang, Y. Existence and boundedness of solutions to maximal monotone inclusion problem. Optim Lett 11, 1565–1570 (2017). https://doi.org/10.1007/s11590-016-1064-y

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  • DOI: https://doi.org/10.1007/s11590-016-1064-y

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