A note on the convergence of barrier algorithms to second-order necessary points

A note on the convergence of barrier algorithms to second-order necessary points

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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: ,
Abstract:

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.

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