Generalized monotone maps. (English) Zbl 1086.49018
Hadjisavvas, Nicolas (ed.) et al., Handbook of generalized convexity and generalized monotonicity. New York, NY: Springer (ISBN 0-387-23255-9/hbk). Nonconvex Optimization and its Applications 76, 389-420 (2005).
The authors present nine kinds of (generalized) monotone maps and in case of gradient maps their counterpart of nine kinds of (generalized) convex functions. Moreover, they present topologically pseudomonotone maps. In the paper there are derived sufficient and/or necessary conditions for various kinds of generalized monotonicity for several subclasses of maps. There are studied differentiable maps, locally Lipschitz maps, general continuous maps and affine maps.
For the entire collection see [Zbl 1070.26002].
For the entire collection see [Zbl 1070.26002].
Reviewer: Stefan Mititelu (Bucureşti)
MSC:
| 49J52 | Nonsmooth analysis |
| 26A48 | Monotonic functions, generalizations |
| 26B25 | Convexity of real functions of several variables, generalizations |
