TY - JOUR
T1 - Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps
AU - Ocaña, Eladio
AU - Cotrina, John
AU - Bueno, Orestes
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
KW - affine multivalued maps
KW - cyclic monotonicity
KW - cyclic quasimonotonicity
KW - index of asymmetry
KW - monotonicity<sup>+</sup>
KW - paramonotonicity
KW - positive semidefinite matrices
KW - affine multivalued maps
KW - cyclic monotonicity
KW - cyclic quasimonotonicity
KW - index of asymmetry
KW - monotonicity<sup>+</sup>
KW - paramonotonicity
KW - positive semidefinite matrices
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84929027780&origin=inward
U2 - 10.1080/02331934.2014.891031
DO - 10.1080/02331934.2014.891031
M3 - Article in a journal
SN - 0233-1934
VL - 64
SP - 1487
EP - 1497
JO - Optimization
JF - Optimization
IS - 7
ER -