Variational methods in convex analysis. (English) Zbl 1103.49005
The authors use variational arguments, namely minimization arguments and decoupling mechanisms, to derive some fundamental theorems in convex analysis. Many important result in linear functional analysis can then be deduced as special cases.
Reviewer: Riccardo De Arcangelis (Napoli)
MSC:
| 49J27 | Existence theories for problems in abstract spaces |
| 46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |
| 49N15 | Duality theory (optimization) |
References:
| [3] | Borwein, J.M. (2006), Maximal monotonicity via convex analysis, to appear in PAMS. · Zbl 1111.47042 |
| [4] | Borwein, J.M. (2006), Maximal monotonicity via convex analysis, J. Convex Analysis, in press. · Zbl 1111.47042 |
| [10] | Fitzpatrick, S. (1988), Representing monotone operators by convex functions. Work-shop/Miniconference on Functional Analysis and Optimization (Canberra, 1988), Proc. Centre Math. Anal. Austral. Nat. Univ., 20, Austral. Nat. Univ., Canberra, pp. 59–65. |
| [14] | Reich, S. and Simons, S. (2004), Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem, preprint. · Zbl 1075.46020 |
| [18] | Simons, S., (2003), ”A new version of the Hahn-Banach theorem,” www.math.ucsb. edu/simons/preprints/. · Zbl 1040.46004 |
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