Optimality Conditions for Multiobjective Optimization Problems via Image Space Analysis

In this article, optimality conditions on (weak) efficient solutions in multiobjective optimization problems are investigated by using the image space analysis. A class of strong separation functions is constructed by oriented distance functions. Simultaneously, a generalized Lagrange function is in...

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Veröffentlicht in:Numerical functional analysis and optimization Jg. 44; H. 7; S. 708 - 723
Hauptverfasser: Xu, Yingrang, Li, Shengjie
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 19.05.2023
Taylor & Francis Ltd
Schlagworte:
90C29
90C46
Generalized KKT necessary conditions
image space analysis
Lagrangian-type sufficient conditions
Multiple objective analysis
Optimization
Separation
strong separation function
ISSN:0163-0563, 1532-2467
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Abstract In this article, optimality conditions on (weak) efficient solutions in multiobjective optimization problems are investigated by using the image space analysis. A class of strong separation functions is constructed by oriented distance functions. Simultaneously, a generalized Lagrange function is introduced by the class of strong separation functions. Then, generalized Karush-Kuhn-Tucker (KKT for short) necessary optimality conditions are established without constraint qualifications or regularity conditions. Under the suitable assumptions, Lagrangian-type sufficient optimality conditions are also characterized. Moreover, the difference between strong separation and weak separation methods is explained.
AbstractList In this article, optimality conditions on (weak) efficient solutions in multiobjective optimization problems are investigated by using the image space analysis. A class of strong separation functions is constructed by oriented distance functions. Simultaneously, a generalized Lagrange function is introduced by the class of strong separation functions. Then, generalized Karush-Kuhn-Tucker (KKT for short) necessary optimality conditions are established without constraint qualifications or regularity conditions. Under the suitable assumptions, Lagrangian-type sufficient optimality conditions are also characterized. Moreover, the difference between strong separation and weak separation methods is explained.
Author Xu, Yingrang
Li, Shengjie
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  surname: Li
  fullname: Li, Shengjie
  organization: College of Mathematics and Statistics, Chongqing University
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SubjectTerms 90C29
90C46
Generalized KKT necessary conditions
image space analysis
Lagrangian-type sufficient conditions
Multiple objective analysis
Optimization
Separation
strong separation function
Title Optimality Conditions for Multiobjective Optimization Problems via Image Space Analysis
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