TY - JOUR
T1 - Strong subdifferentials
T2 - theory and applications in nonconvex optimization
AU - Kabgani, A.
AU - Lara, F.
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/10
Y1 - 2022/10
N2 - A new subdifferential for dealing with nonconvex functions is provided in the following paper and the usual properties are presented as well. Furthermore, characterizations and optimality conditions for a point to be a solution for the nonconvex minimization problem are given. In particular, new KKT-type optimality conditions for nonconvex nonsmooth constraint optimization problems are developed. Moreover, a relationship with the proximity operator for lower semicontinuous quasiconvex functions is given and, as a consequence, the nonemptiness of this subdifferential for large classes of quasiconvex functions is ensured.
AB - A new subdifferential for dealing with nonconvex functions is provided in the following paper and the usual properties are presented as well. Furthermore, characterizations and optimality conditions for a point to be a solution for the nonconvex minimization problem are given. In particular, new KKT-type optimality conditions for nonconvex nonsmooth constraint optimization problems are developed. Moreover, a relationship with the proximity operator for lower semicontinuous quasiconvex functions is given and, as a consequence, the nonemptiness of this subdifferential for large classes of quasiconvex functions is ensured.
KW - Generalized convexity
KW - KKT conditions
KW - Nonconvex optimization
KW - Nonsmooth optimization
KW - Proximal operators
UR - https://www.scopus.com/pages/publications/85126514670
U2 - 10.1007/s10898-022-01149-9
DO - 10.1007/s10898-022-01149-9
M3 - Article
AN - SCOPUS:85126514670
SN - 0925-5001
VL - 84
SP - 349
EP - 368
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 2
ER -