Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps

GuoLin Yu

doi:10.3934/naco.2016.6.35

Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps

Numerical Algebra Control and Optimization ◽

10.3934/naco.2016.6.35 ◽

2016 ◽

Vol 6 (1) ◽

pp. 35-44

Author(s):

GuoLin Yu

Keyword(s):

Vector Optimization ◽

Proper Efficiency ◽

Connected Set ◽

Arcwise Connected

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OPTIMALITY OF GLOBAL PROPER EFFICIENCY FOR CONE-ARCWISE CONNECTED SET-VALUED OPTIMIZATION USING CONTINGENT EPIDERIVATIVE

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595913400046 ◽

2013 ◽

Vol 30 (03) ◽

pp. 1340004 ◽

Cited By ~ 2

Author(s):

GUOLIN YU

Keyword(s):

Optimality Conditions ◽

Optimization Problem ◽

Vector Optimization Problem ◽

Proper Efficiency ◽

Sufficient Optimality Conditions ◽

Set Valued Mapping ◽

Contingent Epiderivative ◽

Connected Set ◽

Arcwise Connected ◽

Necessary And Sufficient

This note deals with the optimality conditions of set-valued unconstraint optimization problem in real normed linear spaces. Based upon the concept of contingent epiderivative, the unified necessary and sufficient optimality conditions for global proper efficiency in vector optimization problem involving cone-arcwise connected set-valued mapping are presented.

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Characterization of the Benson Proper Efficiency and Scalarization in Nonconvex Vector Optimization

Lecture Notes in Economics and Mathematical Systems - Multiple Criteria Decision Making in the New Millennium ◽

10.1007/978-3-642-56680-6_17 ◽

2001 ◽

pp. 189-198 ◽

Cited By ~ 21

Author(s):

Rafail N. Gasimov

Keyword(s):

Vector Optimization ◽

Proper Efficiency ◽

Benson Proper Efficiency ◽

Nonconvex Vector Optimization

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Definition and Characterization of Geoffrion Proper Efficiency for Real Vector Optimization with Infinitely Many Criteria

Journal of Optimization Theory and Applications ◽

10.1007/s10957-014-0608-5 ◽

2014 ◽

Vol 165 (2) ◽

pp. 439-457 ◽

Cited By ~ 11

Author(s):

Alexander Engau

Keyword(s):

Vector Optimization ◽

Proper Efficiency ◽

Real Vector

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Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Journal of Shanghai University (English Edition) ◽

10.1007/s11741-010-0662-3 ◽

2010 ◽

Vol 14 (5) ◽

pp. 374-379 ◽

Cited By ~ 1

Author(s):

Zhi-ang Zhou

Keyword(s):

Vector Optimization ◽

Proper Efficiency ◽

Linear Spaces ◽

Benson Proper Efficiency ◽

Ordered Linear Spaces

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Geoffrion’s proper efficiency in linear fractional vector optimization with unbounded constraint sets

Journal of Global Optimization ◽

10.1007/s10898-020-00927-7 ◽

2020 ◽

Vol 78 (3) ◽

pp. 545-562

Author(s):

N. T. T. Huong ◽

J.-C. Yao ◽

N. D. Yen

Keyword(s):

Vector Optimization ◽

Proper Efficiency ◽

Constraint Sets

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Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization

Journal of Optimization Theory and Applications ◽

10.1007/s10957-008-9414-2 ◽

2008 ◽

Vol 139 (2) ◽

pp. 243-261 ◽

Cited By ~ 24

Author(s):

P. Q. Khanh ◽

N. D. Tuan

Keyword(s):

Optimality Conditions ◽

Vector Optimization ◽

Higher Order ◽

Proper Efficiency ◽

Nonsmooth Vector Optimization ◽

Variational Sets

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Strong Duality for Proper Efficiency in Vector Optimization

Journal of Optimization Theory and Applications ◽

10.1007/s10957-006-9094-8 ◽

2006 ◽

Vol 130 (1) ◽

pp. 139-151 ◽

Cited By ~ 6

Author(s):

P. H. Sach ◽

D. S. Kim ◽

G. M. Lee

Keyword(s):

Vector Optimization ◽

Strong Duality ◽

Proper Efficiency

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Approximating families of cones and proper efficiency in vector optimization

Optimization ◽

10.1080/02331938908843501 ◽

1989 ◽

Vol 20 (6) ◽

pp. 809-817 ◽

Cited By ~ 8

Author(s):

Alicia Sterna-Karwat

Keyword(s):

Vector Optimization ◽

Proper Efficiency

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Proper efficiency for set-valued vector optimization problems and vector variational inequalitiesRID=""ID="" This research was partially supported by the National Natural Science Foundation of P.R. China and the Natural Science Foundation of Jiangxi Province, P.R. China.

Mathematical Methods of Operations Research ◽

10.1007/pl00003994 ◽

2000 ◽

Vol 51 (3) ◽

pp. 443-457 ◽

Cited By ~ 14

Author(s):

Wei Liu ◽

Xunhua Gong

Keyword(s):

Vector Optimization ◽

Natural Science ◽

Optimization Problems ◽

Proper Efficiency ◽

Vector Optimization Problems ◽

Jiangxi Province

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A note on approximate proper efficiency in linear fractional vector optimization

Optimization Letters ◽

10.1007/s11590-021-01806-0 ◽

2021 ◽

Author(s):

Nguyen Van Tuyen

Keyword(s):

Vector Optimization ◽

Proper Efficiency

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Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps

OPTIMALITY OF GLOBAL PROPER EFFICIENCY FOR CONE-ARCWISE CONNECTED SET-VALUED OPTIMIZATION USING CONTINGENT EPIDERIVATIVE

Characterization of the Benson Proper Efficiency and Scalarization in Nonconvex Vector Optimization

Definition and Characterization of Geoffrion Proper Efficiency for Real Vector Optimization with Infinitely Many Criteria

Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Geoffrion’s proper efficiency in linear fractional vector optimization with unbounded constraint sets

Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization

Strong Duality for Proper Efficiency in Vector Optimization

Approximating families of cones and proper efficiency in vector optimization

Proper efficiency for set-valued vector optimization problems and vector variational inequalitiesRID="*"ID="*" This research was partially supported by the National Natural Science Foundation of P.R. China and the Natural Science Foundation of Jiangxi Province, P.R. China.

A note on approximate proper efficiency in linear fractional vector optimization

Proper efficiency for set-valued vector optimization problems and vector variational inequalitiesRID=""ID="" This research was partially supported by the National Natural Science Foundation of P.R. China and the Natural Science Foundation of Jiangxi Province, P.R. China.