other · Contemporary mathematics - American Mathematical Society · 2012

On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function

Heinz H. Bauschke, Xianfu Wang, Liangjin Yao

Cited by 13Abstract and details only

Abstract

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar’s constraint qualification holds. In this note, we provide a new maximal monotonicity result for the sum of a maximal monotone linear relation and the subdifferential operator of a proper, lower semicontinuous, sublinear function. The proof relies on Rockafellar’s formula for the Fenchel conjugate of the sum as well as some results on the Fitzpatrick function.

Cite this paper

APA 7

Bauschke, H. H., Wang, X., & Yao, L. (2012). On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function. Contemporary mathematics - American Mathematical Society, 19–26. https://doi.org/10.1090/conm/568/11273

MLA 9

Bauschke, Heinz H., et al. “On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function.” Contemporary mathematics - American Mathematical Society, 2012, pp. 19–26, https://doi.org/10.1090/conm/568/11273.

Chicago

Bauschke, Heinz H., Xianfu Wang, and Liangjin Yao. 2012. “On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function.” Contemporary mathematics - American Mathematical Society: 19–26. https://doi.org/10.1090/conm/568/11273.

Harvard

Bauschke, H.H., Wang, X. and Yao, L. (2012) ‘On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function’, Contemporary mathematics - American Mathematical Society, pp. 19–26. Available at: https://doi.org/10.1090/conm/568/11273.

BibTeX

@misc{bauschke2012maximal,
  title = {{On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function}},
  author = {Bauschke, Heinz H. and Wang, Xianfu and Yao, Liangjin},
  journal = {Contemporary mathematics - American Mathematical Society},
  pages = {19--26},
  year = {2012},
  doi = {10.1090/conm/568/11273}
}

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