TY - JOUR
T1 - A note on the convergence of barrier algorithms to second-order necessary points
AU - Gould, Nick
AU - Toint, Philippe
N1 - Copyright 2006 Elsevier B.V., All rights reserved.
PY - 1999/1/1
Y1 - 1999/1/1
N2 - It has long been known that barrier algorithms for constrained optimization can produce a sequence of iterates converging to a critical point satisfying weak second-order necessary optimality conditions, when their inner iterations ensures that second-order necessary conditions hold at each barrier minimizer. We show that, despite this, strong second-order necessary conditions may fail to be attained at the limit, even if the barrier minimizers satisfy second-order sufficient optimality conditions.
AB - It has long been known that barrier algorithms for constrained optimization can produce a sequence of iterates converging to a critical point satisfying weak second-order necessary optimality conditions, when their inner iterations ensures that second-order necessary conditions hold at each barrier minimizer. We show that, despite this, strong second-order necessary conditions may fail to be attained at the limit, even if the barrier minimizers satisfy second-order sufficient optimality conditions.
UR - http://www.scopus.com/inward/record.url?scp=0037572858&partnerID=8YFLogxK
U2 - 10.1007/s10107980030a
DO - 10.1007/s10107980030a
M3 - Article
AN - SCOPUS:0037572858
SN - 0025-5610
VL - 85
SP - 433
EP - 438
JO - Mathematical Programming Series B
JF - Mathematical Programming Series B
IS - 2
ER -