Nonlinear constrained optimization of Schur test functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914079027757056 |
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| author | Anikushin, Mikhail Romanov, Andrey |
| author_facet | Anikushin, Mikhail Romanov, Andrey |
| contents | We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such bounds for transfer operators associated with twofold additive compound operators that arise in the study of delay equations. This is related to the verification of frequency inequalities that guarantee the global stability of nonlinear delay equations through the generalized Bendixson criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear constrained optimization of Schur test functions Anikushin, Mikhail Romanov, Andrey Optimization and Control Dynamical Systems 37L15, 90C26, 90C30, 90C90 We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such bounds for transfer operators associated with twofold additive compound operators that arise in the study of delay equations. This is related to the verification of frequency inequalities that guarantee the global stability of nonlinear delay equations through the generalized Bendixson criterion. |
| title | Nonlinear constrained optimization of Schur test functions |
| topic | Optimization and Control Dynamical Systems 37L15, 90C26, 90C30, 90C90 |
| url | https://arxiv.org/abs/2510.05585 |