TY - JOUR
T1 - Second-order asymptotic analysis for noncoercive convex optimization
AU - Lara, F.
N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - We use second-order asymptotic analysis to deal with the minimization problem of a noncoercive convex function in a reflexive Banach space. To that end, we first introduce the definition of a second-order asymptotic cone, and its respective function, based on previous results for the finite dimensional case. We provide necessary and sufficient conditions for the existence of solutions for noncoercive convex minimization problems. Examples for which our assumptions are easier to verify than other well-known results are also provided.
AB - We use second-order asymptotic analysis to deal with the minimization problem of a noncoercive convex function in a reflexive Banach space. To that end, we first introduce the definition of a second-order asymptotic cone, and its respective function, based on previous results for the finite dimensional case. We provide necessary and sufficient conditions for the existence of solutions for noncoercive convex minimization problems. Examples for which our assumptions are easier to verify than other well-known results are also provided.
KW - Asymptotic cones and functions
KW - Convex optimization
KW - Optimality conditions
KW - Second-order asymptotic functions
UR - https://www.scopus.com/pages/publications/85026841836
U2 - 10.1007/s00186-017-0605-1
DO - 10.1007/s00186-017-0605-1
M3 - Article
AN - SCOPUS:85026841836
SN - 1432-2994
VL - 86
SP - 469
EP - 483
JO - Mathematical Methods of Operations Research
JF - Mathematical Methods of Operations Research
IS - 3
ER -