The Augmented Lagrangian Method for Mathematical Programs with Vertical Complementarity Constraints Based on Inexact Scholtes Regularization

Na Xu (), Fan-Yun Meng and Li-Ping Pang ()
Additional contact information
Na Xu: School of Mathematics, Liaoning Normal University, Dalian 116029, P. R. China
Fan-Yun Meng: School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, P. R. China
Li-Ping Pang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 06, 1-31

Abstract: Mathematical program with vertical complementarity constraints (MPVCC) plays an important role in economics and engineering. Due to the vertical complementarity structure, most of the standard constraint qualifications fail to hold at a feasible point. Without constraint qualifications, the Karush–Kuhn–Tucker (KKT) conditions are not necessary optimality conditions. The classical methods for solving constrained optimization problems applied to MPVCC are likely to fail. It is necessary to establish efficient algorithms for solving MPVCC from both theoretical and numerical points of view. We present an algorithm to obtain stationarity of MPVCC by solving a sequence of Scholtes regularized problems. We consider the Scholtes regularization method with the sequence of approximate KKT points only. We prove that, under strictly weaker constraint qualifications, the accumulation point of the approximate KKT points is Clarke (C-) stationary point. In particular, we can get Mordukhovich (M-) or strongly (S-) stationary point under additional assumptions. From these results, we apply an augmented Lagrangian method to obtain a solution of MPVCC and give the convergence analysis. In particular, the accumulation point of the generated iterates is an S-stationary point if some boundedness conditions hold. The numerical results show that it is an effective way to solve MPVCC.

Keywords: Mathematical program with vertical complementarity constraints; C-/M-/S-stationarity; inexact regularization method; augmented Lagrangian method (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595922500427
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:40:y:2023:i:06:n:s0217595922500427

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595922500427

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().