Indirect methods in optimal control on Banach spaces

Fuente: arXiv
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Main Authors: Chertovskih, Roman, Pogodaev, Nikolay, Staritsyn, Maxim, Aguiar, A. Pedro
Format: Preprint
Published: 2025
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_version_ 1866914195504627712
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
id 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