TY - JOUR
T1 - Optimality conditions for convex problems on intersections of non necessarily convex sets
AU - Allevi, E.
AU - Riccardi, R.
AU - Martínez Legaz, Juan Enrique
N1 - We are grateful to Regina S. Burachik for helpful discussions on the notion of local normal cone. We also thank two anonymous reviewers by their useful corrections and remarks, which helped us to improve the presentation; in particular, one of them provided us with the current simplified proof of Lemma
PY - 2019/10/25
Y1 - 2019/10/25
N2 - We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500-510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.
AB - We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500-510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.
KW - Convex optimization
KW - Nonsmooth optimization
KW - Optimality conditions
UR - https://www.scopus.com/pages/publications/85074397681
U2 - 10.1007/s10898-019-00849-z
DO - 10.1007/s10898-019-00849-z
M3 - Article
SN - 0925-5001
VL - 77
SP - 143
EP - 155
JO - Journal of Global Optimization
JF - Journal of Global Optimization
ER -