A Derivative-Free Method with the Symmetric Rank-One Update for Constrained Nonlinear Systems of Monotone Equations Article Swipe
This paper presents a new derivative-free method with a symmetric rank-one (SR1) update for handling constrained nonlinear systems of monotone equations. Distinctively, the approach employs a revised SR1 update formula that leverages information from the latest three iterates and their corresponding function values—a key improvement over existing SR1 variants relying only on two-point information. Derived from this revised formula, the approach integrates projection techniques for performance enhancement. One of its key advantages lies in the search direction: it exhibits sufficient descent and trust-region properties while eliminating the need for line search techniques. Theoretical analysis shows that the algorithm converges globally under specified conditions. Furthermore, numerical experiments are conducted to compare the proposed algorithm with two other existing approaches; results demonstrate that it exhibits superior reliability and robustness in terms of the number of iterations, function evaluations, and CPU runtime.
Related Topics
Concepts
Robustness (evolution)
Line search
Monotone polygon
Iterated function
Nonlinear system
Key (lock)
Mathematical optimization
Computer science
Descent (aeronautics)
Iterated function system
Function (biology)
Mathematics
Reliability (semiconductor)
Projection method
Algorithm
Projection (relational algebra)
Applied mathematics
Descent direction
Line (geometry)
Numerical analysis
Newton's method
Gradient descent
Iterated local search
Coordinate descent
Monotonic function
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/sym17111956
- OA Status
- gold
- References
- 32
- OpenAlex ID
- https://openalex.org/W7105658161
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7105658161Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/sym17111956Digital Object Identifier
- Title
-
A Derivative-Free Method with the Symmetric Rank-One Update for Constrained Nonlinear Systems of Monotone EquationsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-14Full publication date if available
- Authors
-
Xiaowei FangList of authors in order
- Landing page
-
https://doi.org/10.3390/sym17111956Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.3390/sym17111956Direct OA link when available
- Concepts
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Robustness (evolution), Line search, Monotone polygon, Iterated function, Nonlinear system, Key (lock), Mathematical optimization, Computer science, Descent (aeronautics), Iterated function system, Function (biology), Mathematics, Reliability (semiconductor), Projection method, Algorithm, Projection (relational algebra), Applied mathematics, Descent direction, Line (geometry), Numerical analysis, Newton's method, Gradient descent, Iterated local search, Coordinate descent, Monotonic functionTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
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32Number of works referenced by this work
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| abstract_inverted_index.advantages | 71 |
| abstract_inverted_index.direction: | 76 |
| abstract_inverted_index.equations. | 20 |
| abstract_inverted_index.integrates | 61 |
| abstract_inverted_index.projection | 62 |
| abstract_inverted_index.properties | 83 |
| abstract_inverted_index.robustness | 126 |
| abstract_inverted_index.sufficient | 79 |
| abstract_inverted_index.techniques | 63 |
| abstract_inverted_index.values—a | 42 |
| abstract_inverted_index.Theoretical | 92 |
| abstract_inverted_index.approaches; | 117 |
| abstract_inverted_index.conditions. | 102 |
| abstract_inverted_index.constrained | 15 |
| abstract_inverted_index.demonstrate | 119 |
| abstract_inverted_index.eliminating | 85 |
| abstract_inverted_index.experiments | 105 |
| abstract_inverted_index.improvement | 44 |
| abstract_inverted_index.information | 32 |
| abstract_inverted_index.iterations, | 133 |
| abstract_inverted_index.performance | 65 |
| abstract_inverted_index.reliability | 124 |
| abstract_inverted_index.techniques. | 91 |
| abstract_inverted_index.Furthermore, | 103 |
| abstract_inverted_index.enhancement. | 66 |
| abstract_inverted_index.evaluations, | 135 |
| abstract_inverted_index.information. | 53 |
| abstract_inverted_index.trust-region | 82 |
| abstract_inverted_index.corresponding | 40 |
| abstract_inverted_index.Distinctively, | 21 |
| abstract_inverted_index.derivative-free | 5 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile.value | 0.85233881 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |