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Structure Theory for Maximally Monotone Operators with Points of Continuity

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  • Jonathan M. Borwein

    (University of Newcastle)

  • Liangjin Yao

    (University of Newcastle)

Abstract

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of norm-to-weak∗ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.

Suggested Citation

  • Jonathan M. Borwein & Liangjin Yao, 2013. "Structure Theory for Maximally Monotone Operators with Points of Continuity," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 1-24, April.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:1:d:10.1007_s10957-012-0162-y
    DOI: 10.1007/s10957-012-0162-y
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    References listed on IDEAS

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    1. Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, December.
    2. Regina S. Burachik & Alfredo N. Iusem, 2008. "Enlargements of Monotone Operators," Springer Optimization and Its Applications, in: Set-Valued Mappings and Enlargements of Monotone Operators, chapter 0, pages 161-220, Springer.
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    Cited by:

    1. Bao Tran Nguyen & Pham Duy Khanh, 2020. "Faces and Support Functions for the Values of Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 843-863, September.
    2. Bao T. Nguyen & Tran N. Nguyen & Huynh M. Hien, 2024. "Representations for Maximal Monotone Operators of Type (D) in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 1-19, October.

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