Optimality Conditions for Control Systems Governed by Monotone Stochastic Evolution Equations

2025/12/23 by Ioana Ciotir, Nicolas Forcadel, Ciotir, Ioana +5
Computer Science · Economics, Econometrics and Finance · #35R60 #49K30 #60H15 #93E20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2512.20505

openalex publication_date 2025/12/23 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28

Abstract

We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin principle can be recovered in the case that the diffusion doesn't depend on the control. We give several applications, most notably for stochastic porous media equations in the Lipschitz case.

Citations

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Related

• Existence of optimal controls for SPDE with locally monotone\n coefficients
• Necessary Conditions for Optimal Control of SPDE with locally monotone coefficients
• Second Order Optimality Conditions for Optimal Control Problems of Stochastic Evolution Equations
• A Maximum Principle for Optimal Control of Stochastic Evolution Equations
• A stochastic maximum principle of mean-field type with monotonicity conditions