Indirect methods in optimal control on Banach spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914195504627712 |
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| author | Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro |
| author_facet | Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro |
| contents | This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As a reference line, we revisit the classical schemes, rooted in Pontryagin's maximum principle, and highlight their sensitivity to local convexity and lack of monotone convergence. We then develop an alternative method based on exact cost-increment formulas and finite-difference probes of the terminal cost. We show that our method exhibits stable monotone convergence in numerical analysis of an Amari-type neural field control problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indirect methods in optimal control on Banach spaces Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro Optimization and Control Numerical Analysis 49M05, 49K27, 49J20, 92B20, 65K10, 35Q92, 92C20 This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As a reference line, we revisit the classical schemes, rooted in Pontryagin's maximum principle, and highlight their sensitivity to local convexity and lack of monotone convergence. We then develop an alternative method based on exact cost-increment formulas and finite-difference probes of the terminal cost. We show that our method exhibits stable monotone convergence in numerical analysis of an Amari-type neural field control problem. |
| title | Indirect methods in optimal control on Banach spaces |
| topic | Optimization and Control Numerical Analysis 49M05, 49K27, 49J20, 92B20, 65K10, 35Q92, 92C20 |
| url | https://arxiv.org/abs/2512.10831 |