An Implementable Active‐Set Algorithm for Computing a B‐Stationary Point of a Mathematical Program with Linear Complementarity Constraints: Erratum

In [M. Fukushima and P. Tseng, SIAM J. Optim., 12 (2002), pp. 724-739], an ε-active set algorithm was proposed for solving a mathematical program with a smooth objective function and linear inequality/complementarity constraints. It is asserted therein that, under a uniform LICQ on the ε-feasible se...

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Vydáno v:SIAM journal on optimization Ročník 17; číslo 4; s. 1253 - 1257
Hlavní autoři: Fukushima, Masao, Tseng, Paul
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
Témata:
Algorithms
Applied mathematics
Sherman Antitrust Act 1890-US
ISSN:1052-6234, 1095-7189
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Abstract In [M. Fukushima and P. Tseng, SIAM J. Optim., 12 (2002), pp. 724-739], an ε-active set algorithm was proposed for solving a mathematical program with a smooth objective function and linear inequality/complementarity constraints. It is asserted therein that, under a uniform LICQ on the ε-feasible set, this algorithm generates iterates whose cluster points are B-stationary points of the problem. However, the proof has a gap and shows only that each cluster point is an M-stationary point. We discuss this gap and show that B-stationarity can be achieved if the algorithm is modified and an additional error bound condition holds.
AbstractList In [M. Fukushima and P. Tseng, SIAM J. Optim., 12 (2002), pp. 724-739], an ε-active set algorithm was proposed for solving a mathematical program with a smooth objective function and linear inequality/complementarity constraints. It is asserted therein that, under a uniform LICQ on the ε-feasible set, this algorithm generates iterates whose cluster points are B-stationary points of the problem. However, the proof has a gap and shows only that each cluster point is an M-stationary point. We discuss this gap and show that B-stationarity can be achieved if the algorithm is modified and an additional error bound condition holds.
Author Fukushima, Masao
Tseng, Paul
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crossref_primary_10_1007_s13675_015_0044_9
crossref_primary_10_1137_120868359
crossref_primary_10_1007_s11228_009_0112_5
Cites_doi 10.1287/moor.24.3.627
10.1137/S1052623499363232
10.1287/moor.25.1.1.15213
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Sherman Antitrust Act 1890-US
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