TY - JOUR
T1 - Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials
AU - Lara, Felipe
AU - López, Rubén
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - The q-asymptotic function is a new tool that permits to study nonconvex optimization problems with unbounded data. It is particularly useful when dealing with quasiconvex functions. In this paper, we obtain formulas for the q-asymptotic function via c-conjugates, directional derivatives and subdifferentials. We obtain them under lower semicontinuity or local Lipschitz assumptions. The well-known formulas for the asymptotic function in the convex case are consequences of these ones. We obtain a new formula for the convex case.
AB - The q-asymptotic function is a new tool that permits to study nonconvex optimization problems with unbounded data. It is particularly useful when dealing with quasiconvex functions. In this paper, we obtain formulas for the q-asymptotic function via c-conjugates, directional derivatives and subdifferentials. We obtain them under lower semicontinuity or local Lipschitz assumptions. The well-known formulas for the asymptotic function in the convex case are consequences of these ones. We obtain a new formula for the convex case.
KW - Asymptotic cones and functions
KW - Directional derivatives
KW - Subdifferentials
KW - c-Conjugates
KW - q-Asymptotic functions
UR - https://www.scopus.com/pages/publications/85015654285
U2 - 10.1007/s10957-017-1101-8
DO - 10.1007/s10957-017-1101-8
M3 - Article
AN - SCOPUS:85015654285
SN - 0022-3239
VL - 173
SP - 793
EP - 811
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -