Monotone Operators and "Bigger Conjugate" Functions

Bauschke, Heinz H. and Borwein, Jonathan M. and Wang, Xianfu and Yao, Liangjin (2013) Monotone Operators and "Bigger Conjugate" Functions. Journal of Convex Analysis, 20 (1). pp. 143-155.

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    We study a question posed by Stephen Simons in his 2008 monograph involving "bigger conjugate" (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools for further analysis of BC-functions which allow us to answer Simons' problem in the negative. We are also able to refute a similar but much harder conjecture which would have generalized a classical result of Brézis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.

    Item Type: Article
    Uncontrolled Keywords: Adjoint, BC-function, Fenchel conjugate, Fitzpatrick function, linear relation, maximally monotone operator, monotone operator, multifunction, normal cone operator, partial infimal convolution
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 12 Jun 2013 14:29
    Last Modified: 14 Aug 2013 15:14

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