Article ID: | iaor20001818 |
Country: | Germany |
Volume: | 85 |
Issue: | 2 |
Start Page Number: | 433 |
End Page Number: | 438 |
Publication Date: | Jan 1999 |
Journal: | Mathematical Programming |
Authors: | Gould N.I.M., Toint P.L. |
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 ensure that second-order necessary conditions hold at each barrier minimizer. We show that, despite this, strong-order necessary conditions may fail to be attained at the limit, even if the barrier minimizers satisfy second-order sufficient optimality conditions.