Abstract
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
References
- J. M. Borwein: A note on ε-subgradients and maximal monotonicity, Pacific J. Math. 103 (1982) 307–314.https://doi.org/10.2140/pjm.1982.103.307Google Scholar
- M. W. Botsko: The teaching of mathematics: a first derivative test for functions of several variables, Amer. Math. Monthly 93 (1986) 558–561.https://doi.org/10.1080/00029890.1986.11971886Google Scholar
- A. Brøndsted, R. T. Rockafellar: On the subdifferentiability of convex functions, Proc. Amer. Math. Soc. 16 (1965) 605–611.https://doi.org/10.1090/S0002-9939-1965-0178103-8Google Scholar
- R. B. Holmes: Geometric Functional Analysis and its Applications, Graduate Texts in Mathematics 24, Springer-Verlag, Berlin (1975).https://doi.org/10.1007/978-1-4684-9369-6Google Scholar
- J.-J. Moreau: Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France 93 (1965) 273–299.https://doi.org/10.24033/bsmf.1625Google Scholar
- F. Jules, M. Lassonde: Subdifferential test for optimality, J. Global Optim. 59 (2014) 101–106.https://doi.org/10.1007/s10898-013-0078-6Google Scholar
- M. Marques Alves, B. F. Svaiter: A new proof for maximal monotonicity of subdifferential operators, J. Convex Analysis 15 (2008) 345–348.https://doi.org/10.68381/jca15024Google Scholar
- G. J. Minty: On the monotonicity of the gradient of a convex function, Pacific J. Math. 14 (1964) 243–247.https://doi.org/10.2140/pjm.1964.14.243Google Scholar
- R. R. Phelps: Convex functions, monotone operators and differentiability, Lecture Notes in Mathematics 1364, Springer-Verlag, Berlin (1989).https://doi.org/10.1007/978-3-662-21569-2Google Scholar
- R. R. Phelps: Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Mathematics 1364, second edition, Springer-Verlag, Berlin (1993).Google Scholar
- R. T. Rockafellar: Characterization of the subdifferentials of convex functions, Pacific J. Math. 17 (1966) 497–510.https://doi.org/10.2140/pjm.1966.17.497Google Scholar
- R. T. Rockafellar: On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970) 209–216.https://doi.org/10.2140/pjm.1970.33.209Google Scholar
- S. Simons: The least slope of a convex function and the maximal monotonicity of its subdifferential, J. Optim. Theory Appl. 71 (1991) 127–136.https://doi.org/10.1007/BF00940043Google Scholar
- S. Simons: A new proof of the maximal monotonicity of subdifferentials, J. Convex Analysis 16 (2009) 165–168.https://doi.org/10.68381/jca16008Google Scholar
- P. D. Taylor: Subgradients of a convex function obtained from a directional derivative, Pacific J. Math. 44 (1973) 739–747.https://doi.org/10.2140/pjm.1973.44.739Google Scholar
- L. Thibault: Limiting convex subdifferential calculus with applications to integration and maximal monotonicity of subdifferential, in: Constructive, Experimental, and Nonlinear Analysis (Limoges, 1999), CMS Conf. Proc. 27, Amer. Math. Soc., Providence (2000) 279–289.Google Scholar
- D. Zagrodny: Approximate mean value theorem for upper subderivatives, Nonlinear Analysis 12 (1988) 1413–1428.https://doi.org/10.1016/0362-546X(88)90088-0Google Scholar
- C. Zălinescu: Convex analysis in general vector spaces, World Scientific, River Edge (2002).https://doi.org/10.1142/5021Google Scholar
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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.
