Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

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

doi:10.1080/02331934.2019.1591406

Some kind of Pareto stationarity 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

8 Citations (Scopus)

Abstract

In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.

Original language	English
Pages (from-to)	1245-1260
Number of pages	16
Journal	Optimization
Volume	68
Issue number	6
DOIs	https://doi.org/10.1080/02331934.2019.1591406
Publication status	Published - 3 Jun 2019

User-Defined Keywords

generalized Guignard constraint qualification
Multiobjective problem with equilibrium constraints
Pareto optimality
S-stationarity
strong Pareto Kuhn-Tucker conditions

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10.1080/02331934.2019.1591406

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title = "Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints",

abstract = "In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.",

keywords = "generalized Guignard constraint qualification, Multiobjective problem with equilibrium constraints, Pareto optimality, S-stationarity, strong Pareto Kuhn-Tucker conditions",

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

note = "Funding Information: This work was supported in part by National Natural Science Foundation of China NSFC (Nos. 11671250, 11431004, 71831008, 11601458) and Humanity Social Science Foundation of Ministry of Education of China (No. 15YJA630034). HKBU FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J. Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2019",

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doi = "10.1080/02331934.2019.1591406",

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T1 - Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

AU - Zhang, Peng

AU - Zhang, Jin

AU - Lin, Gui Hua

AU - Yang, Xinmin

N1 - Funding Information: This work was supported in part by National Natural Science Foundation of China NSFC (Nos. 11671250, 11431004, 71831008, 11601458) and Humanity Social Science Foundation of Ministry of Education of China (No. 15YJA630034). HKBU FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J. Publisher Copyright: © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2019/6/3

Y1 - 2019/6/3

N2 - In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.

AB - In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.

KW - generalized Guignard constraint qualification

KW - Multiobjective problem with equilibrium constraints

KW - Pareto optimality

KW - S-stationarity

KW - strong Pareto Kuhn-Tucker conditions

UR - https://www.scopus.com/pages/publications/85063434959

U2 - 10.1080/02331934.2019.1591406

DO - 10.1080/02331934.2019.1591406

M3 - Journal article

AN - SCOPUS:85063434959

SN - 0233-1934

VL - 68

SP - 1245

EP - 1260

JO - Optimization

JF - Optimization

IS - 6

ER -

Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

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