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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Numerical Methods for Optimal Control Problems with Spdes

Numerical Methods for Optimal Control Problems with Spdes

Prohl, Andreas
Wang, Yanqing

Paperback

Series: Springerbriefs on Pdes and Data Science

General Mathematics

PREORDER - Expected ship date March 3, 2026

ISBN10: 9819544688
ISBN13: 9789819544684
Publisher: Springer
Published: Mar 3 2026
Pages: 133
Language: English
This book is on the construction and convergence analysis of implementable algorithms to approximate the optimal control of a stochastic linear-quadratic optimal control problem (SLQ problem, for short) subject to a stochastic PDE. If compared to finite dimensional stochastic control theory, the increased complexity due to high-dimensionality requires new numerical concepts to approximate SLQ problems; likewise, well-established discretization and numerical optimization strategies from infinite dimensional deterministic control theory need fundamental changes to properly address the optimality system, where to approximate the solution of a backward stochastic PDE is conceptually new. The linear-quadratic structure of SLQ problems allows two equivalent analytical approaches to characterize its minimum: 'open loop' is based on Pontryagin's maximum principle, and 'closed loop' utilizes the stochastic Riccati equation in combination with the feedback control law. The authors will discuss why, in general, complexities of related numerical schemes differ drastically, and when which direction should be given preference from an algorithmic viewpoint.

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