Analyzing the Effect of Persistent Asset Switches on a Class of Hybrid-Inspired Optimization Algorithms
Convex optimization challenges are currently pervasive in many science and engineering domains. In many applications of convex optimization, such as those involving multi-agent systems and resource allocation, the objective function can persistently switch during the execution of an optimization alg...
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| Vydané v: | Proceedings of the American Control Conference s. 3422 - 3427 |
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| Hlavní autori: | , , |
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| Jazyk: | English |
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American Automatic Control Council
25.05.2021
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| ISSN: | 2378-5861 |
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| Abstract | Convex optimization challenges are currently pervasive in many science and engineering domains. In many applications of convex optimization, such as those involving multi-agent systems and resource allocation, the objective function can persistently switch during the execution of an optimization algorithm. Motivated by such applications, we analyze the effect of persistently switching objectives in continuous-time optimization algorithms. In particular, we take advantage of existing robust stability results for switched systems with distinct equilibria and extend these results to systems described by differential inclusions, making the results applicable to recent optimization algorithms that employ differential inclusions for improving efficiency and/or robustness. Within the framework of hybrid systems theory, we provide an accurate characterization, in terms of Omega-limit sets, of the set to which the optimization dynamics converge. Finally, by considering the switching signal to be constrained in its average dwell time, we establish semi-global practical asymptotic stability of these sets with respect to the dwell-time parameter. |
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| AbstractList | Convex optimization challenges are currently pervasive in many science and engineering domains. In many applications of convex optimization, such as those involving multi-agent systems and resource allocation, the objective function can persistently switch during the execution of an optimization algorithm. Motivated by such applications, we analyze the effect of persistently switching objectives in continuous-time optimization algorithms. In particular, we take advantage of existing robust stability results for switched systems with distinct equilibria and extend these results to systems described by differential inclusions, making the results applicable to recent optimization algorithms that employ differential inclusions for improving efficiency and/or robustness. Within the framework of hybrid systems theory, we provide an accurate characterization, in terms of Omega-limit sets, of the set to which the optimization dynamics converge. Finally, by considering the switching signal to be constrained in its average dwell time, we establish semi-global practical asymptotic stability of these sets with respect to the dwell-time parameter. |
| Author | Baradaran, Matina Teel, Andrew R. Le, Justin H. |
| Author_xml | – sequence: 1 givenname: Matina surname: Baradaran fullname: Baradaran, Matina email: baradaranhosseini@ucsb.edu organization: University of California,Department of Electrical and Computer Engineering,Santa Barbara,CA,USA,93106 – sequence: 2 givenname: Justin H. surname: Le fullname: Le, Justin H. email: justinle@ucsb.edu organization: University of California,Department of Electrical and Computer Engineering,Santa Barbara,CA,USA,93106 – sequence: 3 givenname: Andrew R. surname: Teel fullname: Teel, Andrew R. email: teel@ucsb.edu organization: University of California,Department of Electrical and Computer Engineering,Santa Barbara,CA,USA,93106 |
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| Snippet | Convex optimization challenges are currently pervasive in many science and engineering domains. In many applications of convex optimization, such as those... |
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| StartPage | 3422 |
| SubjectTerms | Asymptotic stability Convex functions Heuristic algorithms Linear programming Robust stability Switched systems Switches |
| Title | Analyzing the Effect of Persistent Asset Switches on a Class of Hybrid-Inspired Optimization Algorithms |
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