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/10.48550/arxiv.2401.06351
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.06351
This study delves into equilibrium problems, focusing on the identification of 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, a comprehensive concept that 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 existing literature, which often assumes the solution set to be weakly sharp or strongly non-degenerate, especially in the context of 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
Degeneracy (biology)
Solution set
Degenerate energy levels
Premise
Solution concept
Mathematics
Context (archaeology)
Set (abstract data type)
Variational inequality
Regular polygon
Finite set
Computer science
Optimization problem
Applied mathematics
Mathematical analysis
Physics
Paleontology
Philosophy
Bioinformatics
Linguistics
Programming language
Geometry
Quantum mechanics
Biology
Nash equilibrium
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2401.06351
- https://arxiv.org/pdf/2401.06351
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4390897519
All OpenAlex metadata
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https://openalex.org/W4390897519Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2401.06351Digital Object Identifier
- Title
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The augmented weak sharpness of solution sets in equilibrium problemsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-01-12Full publication date if available
- Authors
-
Ruyu Wang, Wenling Zhao, Daojin Song, Yaozhong HuList of authors in order
- Landing page
-
https://arxiv.org/abs/2401.06351Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2401.06351Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2401.06351Direct OA link when available
- Concepts
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Mathematical optimization, Degeneracy (biology), Solution set, Degenerate energy levels, Premise, Solution concept, Mathematics, Context (archaeology), Set (abstract data type), Variational inequality, Regular polygon, Finite set, Computer science, Optimization problem, Applied mathematics, Mathematical analysis, Physics, Paleontology, Philosophy, Bioinformatics, Linguistics, Programming language, Geometry, Quantum mechanics, Biology, Nash equilibriumTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.weak | 24, 37, 51, 73, 85, 114 |
| abstract_inverted_index.field | 194 |
| abstract_inverted_index.light | 161 |
| abstract_inverted_index.makes | 188 |
| abstract_inverted_index.often | 133 |
| abstract_inverted_index.range | 215 |
| abstract_inverted_index.scope | 128 |
| abstract_inverted_index.sets. | 41 |
| abstract_inverted_index.sharp | 25, 141 |
| abstract_inverted_index.study | 1 |
| abstract_inverted_index.these | 107 |
| abstract_inverted_index.under | 109 |
| abstract_inverted_index.where | 44 |
| abstract_inverted_index.which | 132 |
| abstract_inverted_index.wider | 214 |
| abstract_inverted_index.convex | 29 |
| abstract_inverted_index.delves | 2 |
| abstract_inverted_index.finite | 11, 104, 179 |
| abstract_inverted_index.strong | 88 |
| abstract_inverted_index.weakly | 140 |
| abstract_inverted_index.within | 90 |
| abstract_inverted_index.assumes | 134 |
| abstract_inverted_index.coining | 34 |
| abstract_inverted_index.concept | 27, 81 |
| abstract_inverted_index.context | 148 |
| abstract_inverted_index.exhibit | 50 |
| abstract_inverted_index.mapping | 57 |
| abstract_inverted_index.minimum | 26 |
| abstract_inverted_index.premise | 111 |
| abstract_inverted_index.propose | 54 |
| abstract_inverted_index.various | 182 |
| abstract_inverted_index.approach | 58 |
| abstract_inverted_index.broadens | 126 |
| abstract_inverted_index.existing | 130 |
| abstract_inverted_index.feasible | 14, 91 |
| abstract_inverted_index.findings | 157 |
| abstract_inverted_index.focusing | 6 |
| abstract_inverted_index.identify | 96 |
| abstract_inverted_index.mitigate | 60 |
| abstract_inverted_index.problems | 168, 204 |
| abstract_inverted_index.research | 67 |
| abstract_inverted_index.solution | 15, 40, 46, 77, 92, 118, 136 |
| abstract_inverted_index.strongly | 143 |
| abstract_inverted_index.theories | 211 |
| abstract_inverted_index.augmented | 56, 72, 113 |
| abstract_inverted_index.condition | 101, 124, 176 |
| abstract_inverted_index.enhancing | 196 |
| abstract_inverted_index.expanding | 206 |
| abstract_inverted_index.extension | 21 |
| abstract_inverted_index.introduce | 18, 171 |
| abstract_inverted_index.necessary | 98 |
| abstract_inverted_index.problems, | 5, 33 |
| abstract_inverted_index.problems. | 122, 155 |
| abstract_inverted_index.research, | 186 |
| abstract_inverted_index.sequences | 108 |
| abstract_inverted_index.sharpness | 38, 74, 86, 115 |
| abstract_inverted_index.solutions | 12 |
| abstract_inverted_index.stringent | 174 |
| abstract_inverted_index.Crucially, | 94 |
| abstract_inverted_index.conditions | 165, 201 |
| abstract_inverted_index.especially | 145 |
| abstract_inverted_index.inequality | 154 |
| abstract_inverted_index.innovative | 20 |
| abstract_inverted_index.scenarios. | 218 |
| abstract_inverted_index.sequences. | 16, 93 |
| abstract_inverted_index.sharpness, | 52 |
| abstract_inverted_index.situations | 43 |
| abstract_inverted_index.sufficient | 100, 175 |
| abstract_inverted_index.therefore, | 187 |
| abstract_inverted_index.Recognizing | 42 |
| abstract_inverted_index.algorithms. | 184 |
| abstract_inverted_index.equilibrium | 4, 32, 121, 167, 203 |
| abstract_inverted_index.established | 210 |
| abstract_inverted_index.formulation | 70 |
| abstract_inverted_index.limitation. | 62 |
| abstract_inverted_index.literature, | 131 |
| abstract_inverted_index.programming | 30, 151 |
| abstract_inverted_index.substantial | 190 |
| abstract_inverted_index.termination | 105, 164, 180, 200 |
| abstract_inverted_index.variational | 153 |
| abstract_inverted_index.contribution | 191 |
| abstract_inverted_index.encapsulates | 83 |
| abstract_inverted_index.mathematical | 150 |
| abstract_inverted_index.optimization | 183, 217 |
| abstract_inverted_index.applicability | 208 |
| abstract_inverted_index.comprehensive | 80 |
| abstract_inverted_index.significantly | 125 |
| abstract_inverted_index.understanding | 198 |
| abstract_inverted_index.identification | 9 |
| abstract_inverted_index.non-degeneracy | 89 |
| abstract_inverted_index.non-degenerate, | 144 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |