首页|Partial augmented Lagrangian method for non-Lipschitz mathematical programs with complementarity constraints
Partial augmented Lagrangian method for non-Lipschitz mathematical programs with complementarity constraints
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Springer Nature
In recent years, mathematical programs with complementarity constraints (MPCC) and a non-Lipschitz objective function have been introduced and are now more prevalent than locally Lipschitz MPCC. This paper proposes a smoothing partial augmented Lagrangian (SPAL) method to tackle this problem. However, due to the disruption of the complementary structure's integrity by this method, proving its convergence becomes exceptionally challenging. We have achieved global convergence of the SPAL method. Specifically, we demonstrate that the accumulation point of the sequence generated by the SPAL method can be a strongly stationary point under the Mangasarian-Fromovitz qualification (MPCC-MFQ) and the boundedness of the multiplier corresponding to the orthogonal constraint. Moreover, if the aforementioned multiplier is unbounded, the accumulation point can be a Clarke stationary point under MPCC-MFQ and a suitable assumption. Numerical experiments indicate that the SPAL method surpasses existing methods in terms of the quality of accumulation points and running times.
Mathematical program with complementarity constraintsNon-Lipschitz continuityQualificationAugmented Lagrangian method
Gao-Xi Li、Xin-Min Yang、Xian-Jun Long
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School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China||Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing Technology and Business University, Chongqing 400067, China
School of Mathematics Science, Chongqing Normal University, Chongqing 401331, China
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
NETL
NSTL
Springer Nature
