{"ID":2849290,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.24876","arxiv_id":"2510.24876","title":"Convergence analysis for an implementable scheme to solve the linear-quadratic stochastic optimal control problem with stochastic wave equation","abstract":"We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize the optimal state-control pair via a coupled forward-backward SPDE system. We propose an implementable discretization using conforming finite elements in space and an implicit midpoint rule in time. By a new technical approach we obtain strong convergence rates for the discrete state-control pair without relying on Malliavin calculus. For the practical computation we develop a gradient-descent algorithm based on artificial iterates that employs an exact computation for the arising conditional expectations, thereby eliminating costly Monte Carlo sampling. Consequently, each iteration has a computational cost that is proportional to the number of spatial degrees of freedom, producing a scalable method that preserves the established strong convergence rates. Numerical results validate its efficiency.","short_abstract":"We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize the optimal state-control pair via a coupled forward-backward SPDE system. We pr...","url_abs":"https://arxiv.org/abs/2510.24876","url_pdf":"https://arxiv.org/pdf/2510.24876v1","authors":"[\"Abhishek Chaudhary\"]","published":"2025-10-28T18:25:26Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AP\",\"math.NA\",\"math.PR\"]","methods":"[]","has_code":false}