TY - JOUR
T1 - A Quasiconvex Asymptotic Function with Applications in Optimization
AU - Hadjisavvas, Nicolas
AU - Lara, Felipe
AU - Martínez-Legaz, Juan Enrique
PY - 2019/1/15
Y1 - 2019/1/15
N2 - © 2018, Springer Science+Business Media, LLC, part of Springer Nature. We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.
AB - © 2018, Springer Science+Business Media, LLC, part of Springer Nature. We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.
KW - 90C25
KW - 90C26
KW - 90C30
KW - Asymptotic cones
KW - Asymptotic functions
KW - Closedness criteria
KW - Nonconvex optimization
KW - Quasiconvexity
UR - http://www.mendeley.com/research/quasiconvex-asymptotic-function-applications-optimization
U2 - 10.1007/s10957-018-1317-2
DO - 10.1007/s10957-018-1317-2
M3 - Article
SN - 0022-3239
VL - 180
SP - 170
EP - 186
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -