The Augmented Weak Sharpness of Solution Sets in Equilibrium Problems Article Swipe
Ruyu Wang
,
Wenling Zhao
,
Daojin Song
,
Yaozhong Hu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3390/math12020352
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3390/math12020352
This study considers equilibrium problems, focusing on identifying finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium problems, coining this as weak sharpness for solution sets. Recognizing situations where the solution set may not exhibit weak sharpness, we propose an augmented mapping approach to mitigate this limitation. The core of our research is the formulation of augmented weak sharpness for the solution set. This comprehensive concept encapsulates both weak sharpness and strong non-degeneracy within feasible solution sequences. Crucially, we identify a necessary and sufficient condition for the finite termination of these sequences under the premise of augmented weak sharpness for the solution set in equilibrium problems. This condition significantly broadens the scope of the existing literature, which often assumes the solution set to be weakly sharp or strongly non-degenerate, especially in mathematical programming and variational inequality problems. Our findings not only shed light on the termination conditions in equilibrium problems but also introduce a less stringent sufficient condition for the finite termination of various optimization algorithms. This research, therefore, makes a substantial contribution to the field by enhancing our understanding of termination conditions in equilibrium problems and expanding the applicability of established theories to a wider range of optimization scenarios.
Related Topics
Concepts
Mathematical optimization
Degenerate energy levels
Degeneracy (biology)
Solution set
Solution concept
Premise
Variational inequality
Mathematics
Set (abstract data type)
Finite set
Regular polygon
Optimization problem
Computer science
Applied mathematics
Mathematical analysis
Physics
Geometry
Biology
Programming language
Bioinformatics
Linguistics
Nash equilibrium
Quantum mechanics
Philosophy
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math12020352
- https://www.mdpi.com/2227-7390/12/2/352/pdf?version=1705913247
- OA Status
- gold
- Cited By
- 1
- References
- 38
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4391103088
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4391103088Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/math12020352Digital Object Identifier
- Title
-
The Augmented Weak Sharpness of Solution Sets in Equilibrium ProblemsWork title
- Type
-
articleOpenAlex work type
- Language
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enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-01-22Full publication date if available
- Authors
-
Ruyu Wang, Wenling Zhao, Daojin Song, Yaozhong HuList of authors in order
- Landing page
-
https://doi.org/10.3390/math12020352Publisher landing page
- PDF URL
-
https://www.mdpi.com/2227-7390/12/2/352/pdf?version=1705913247Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://www.mdpi.com/2227-7390/12/2/352/pdf?version=1705913247Direct OA link when available
- Concepts
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Mathematical optimization, Degenerate energy levels, Degeneracy (biology), Solution set, Solution concept, Premise, Variational inequality, Mathematics, Set (abstract data type), Finite set, Regular polygon, Optimization problem, Computer science, Applied mathematics, Mathematical analysis, Physics, Geometry, Biology, Programming language, Bioinformatics, Linguistics, Nash equilibrium, Quantum mechanics, PhilosophyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
- Citations by year (recent)
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2024: 1Per-year citation counts (last 5 years)
- References (count)
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38Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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