Abstract
We prove that the notions of (Formula presented.) -cyclic quasimonotonicity and (Formula presented.) -cyclic monotonicity are equivalent for affine maps defined on Banach spaces. First this is done in a finite dimensional space by using the index of asymmetry for matrices defined by J.-P. Crouzeix and C. Gutan. Then this equivalence is extended to general Banach spaces.
Original language | English |
---|---|
Pages (from-to) | 1487-1497 |
Number of pages | 11 |
Journal | Optimization |
Volume | 64 |
Issue number | 7 |
DOIs | |
State | Published - 1 Jan 2015 |
Keywords
- affine multivalued maps
- cyclic monotonicity
- cyclic quasimonotonicity
- index of asymmetry
- monotonicity<sup>+</sup>
- paramonotonicity
- positive semidefinite matrices