Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints

Suhong Jiang; Jin Zhang; Caihua Chen; Guihua Lin

doi:10.1007/s10898-017-0539-4

Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints

Suhong Jiang
, Jin Zhang
, Caihua Chen
, Guihua Lin^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

8 Citations (Scopus)

Abstract

Mathematical program with equilibrium constraints (MPEC) is an important problem in mathematical programming as it arises frequently in a broad spectrum of fields. In this paper, we propose an implementable smoothing partial exact penalty method to solve MPEC, where the subproblems are solved inexactly by the proximal alternating linearized minimization method. Under the extend MPEC-NNAMCQ, the proposed method is shown to be convergent to an M-stationary point of the MPEC.

Original language	English
Pages (from-to)	223-236
Number of pages	14
Journal	Journal of Global Optimization
Volume	70
Issue number	1
DOIs	https://doi.org/10.1007/s10898-017-0539-4
Publication status	Published - 1 Jan 2018

User-Defined Keywords

M-stationarity
MPEC
Partial penalty method
Proximal alternating linearized minimization method
S-stationarity

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10.1007/s10898-017-0539-4

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title = "Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints",

abstract = "Mathematical program with equilibrium constraints (MPEC) is an important problem in mathematical programming as it arises frequently in a broad spectrum of fields. In this paper, we propose an implementable smoothing partial exact penalty method to solve MPEC, where the subproblems are solved inexactly by the proximal alternating linearized minimization method. Under the extend MPEC-NNAMCQ, the proposed method is shown to be convergent to an M-stationary point of the MPEC.",

keywords = "M-stationarity, MPEC, Partial penalty method, Proximal alternating linearized minimization method, S-stationarity",

author = "Suhong Jiang and Jin Zhang and Caihua Chen and Guihua Lin",

note = "Funding Information: This work was supported in part by NSFC (Nos. 11401300, 11431004, 11671250, 11601458) and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034).",

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doi = "10.1007/s10898-017-0539-4",

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T1 - Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints

AU - Jiang, Suhong

AU - Zhang, Jin

AU - Chen, Caihua

AU - Lin, Guihua

N1 - Funding Information: This work was supported in part by NSFC (Nos. 11401300, 11431004, 11671250, 11601458) and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034).

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Mathematical program with equilibrium constraints (MPEC) is an important problem in mathematical programming as it arises frequently in a broad spectrum of fields. In this paper, we propose an implementable smoothing partial exact penalty method to solve MPEC, where the subproblems are solved inexactly by the proximal alternating linearized minimization method. Under the extend MPEC-NNAMCQ, the proposed method is shown to be convergent to an M-stationary point of the MPEC.

AB - Mathematical program with equilibrium constraints (MPEC) is an important problem in mathematical programming as it arises frequently in a broad spectrum of fields. In this paper, we propose an implementable smoothing partial exact penalty method to solve MPEC, where the subproblems are solved inexactly by the proximal alternating linearized minimization method. Under the extend MPEC-NNAMCQ, the proposed method is shown to be convergent to an M-stationary point of the MPEC.

KW - M-stationarity

KW - MPEC

KW - Partial penalty method

KW - Proximal alternating linearized minimization method

KW - S-stationarity

UR - https://www.scopus.com/pages/publications/85020736990

U2 - 10.1007/s10898-017-0539-4

DO - 10.1007/s10898-017-0539-4

M3 - Journal article

AN - SCOPUS:85020736990

SN - 0925-5001

VL - 70

SP - 223

EP - 236

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 1

ER -

Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints

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