Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations

Weilong You and Fu Zhang ()
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Weilong You: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Fu Zhang: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Mathematics, 2025, vol. 13, issue 7, 1-17

Abstract: This paper applies the Method of Successive Approximations (MSA) based on Pontryagin’s principle to solve optimal control problems with state constraints for semilinear parabolic equations. Error estimates for the first and second derivatives of the function are derived under L ∞ -bounded conditions. An augmented MSA is developed using the augmented Lagrangian method, and its convergence is proven. The effectiveness of the proposed method is demonstrated through numerical experiments.

Keywords: optimal control; parabolic equation; Pontryagin’s principle; MSA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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