TY - JOUR
T1 - Second order optimality conditions based on parabolic second order tangent sets
AU - Bonnans, J. Frédéric
AU - Cominetti, Roberto
AU - Shapiro, Alexander
PY - 1999/3
Y1 - 1999/3
N2 - In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order sufficient conditions. We show that the second order regularity condition always holds in the case of semidefinite programming.
AB - In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order sufficient conditions. We show that the second order regularity condition always holds in the case of semidefinite programming.
KW - Cone constraints
KW - Duality
KW - Lagrange multipliers
KW - Second order optimality conditions
KW - Semi-infinite programming
KW - Semidefinite programming
KW - Tangent sets
UR - http://www.scopus.com/inward/record.url?scp=0033434223&partnerID=8YFLogxK
U2 - 10.1137/S1052623496306760
DO - 10.1137/S1052623496306760
M3 - Article
AN - SCOPUS:0033434223
SN - 1052-6234
VL - 9
SP - 466
EP - 492
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 2
ER -