Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints

Peng Zhang; Jin Zhang; Gui Hua Lin; Xinmin Yang

doi:10.1007/s10957-018-1235-3

Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints

Peng Zhang, Jin Zhang, Gui Hua Lin^*, Xinmin Yang

^*Corresponding author for this work

Department of Mathematics

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

10 Citations (Scopus)

Abstract

In this paper, we consider a class of multiobjective problems with equilibrium constraints. Our first task is to extend the existing constraint qualifications for mathematical problems with equilibrium constraints from the single-objective case to the multiobjective case, and our second task is to derive some stationarity conditions under the proper Pareto sense for the considered problem. After doing that, we devote ourselves to investigating the relationships among the extended constraint qualifications and the proper Pareto stationarity conditions.

Original language	English
Pages (from-to)	763-782
Number of pages	20
Journal	Journal of Optimization Theory and Applications
Volume	176
Issue number	3
DOIs	https://doi.org/10.1007/s10957-018-1235-3
Publication status	Published - 1 Mar 2018

Scopus Subject Areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

User-Defined Keywords

Constraint qualification
Multiobjective problem with equilibrium constraints
Proper Pareto stationarity condition

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10.1007/s10957-018-1235-3

Cite this

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title = "Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints",

abstract = "In this paper, we consider a class of multiobjective problems with equilibrium constraints. Our first task is to extend the existing constraint qualifications for mathematical problems with equilibrium constraints from the single-objective case to the multiobjective case, and our second task is to derive some stationarity conditions under the proper Pareto sense for the considered problem. After doing that, we devote ourselves to investigating the relationships among the extended constraint qualifications and the proper Pareto stationarity conditions.",

keywords = "Constraint qualification, Multiobjective problem with equilibrium constraints, Proper Pareto stationarity condition",

author = "Peng Zhang and Jin Zhang and Lin, {Gui Hua} and Xinmin Yang",

note = "Funding Information: Acknowledgements This work was supported in part by NSFC (Nos. 11671250, 11431004, 11601458), HKBU Grants (Nos. FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J), and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034).",

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doi = "10.1007/s10957-018-1235-3",

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T1 - Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints

AU - Zhang, Peng

AU - Zhang, Jin

AU - Lin, Gui Hua

AU - Yang, Xinmin

N1 - Funding Information: Acknowledgements This work was supported in part by NSFC (Nos. 11671250, 11431004, 11601458), HKBU Grants (Nos. FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J), and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034).

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In this paper, we consider a class of multiobjective problems with equilibrium constraints. Our first task is to extend the existing constraint qualifications for mathematical problems with equilibrium constraints from the single-objective case to the multiobjective case, and our second task is to derive some stationarity conditions under the proper Pareto sense for the considered problem. After doing that, we devote ourselves to investigating the relationships among the extended constraint qualifications and the proper Pareto stationarity conditions.

AB - In this paper, we consider a class of multiobjective problems with equilibrium constraints. Our first task is to extend the existing constraint qualifications for mathematical problems with equilibrium constraints from the single-objective case to the multiobjective case, and our second task is to derive some stationarity conditions under the proper Pareto sense for the considered problem. After doing that, we devote ourselves to investigating the relationships among the extended constraint qualifications and the proper Pareto stationarity conditions.

KW - Constraint qualification

KW - Multiobjective problem with equilibrium constraints

KW - Proper Pareto stationarity condition

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DO - 10.1007/s10957-018-1235-3

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SN - 0022-3239

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JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

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Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints

Abstract

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