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计算数学（英文版）
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2026年6期
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STOCHASTIC PROXIMAL LINEARIZED ADMM FOR SPARSE DISTRIBUTION CONTROL PROBLEM CONSTRAINED BY RANDOM ELLIPTIC EQUATION
STOCHASTIC PROXIMAL LINEARIZED ADMM FOR SPARSE DISTRIBUTION CONTROL PROBLEM CONSTRAINED BY RANDOM ELLIPTIC EQUATION
摘要
In this paper,we consider the sparse distributed control problem constrained by a ran-dom elliptic equation,which we reformulate as a nonsmooth stochastic optimization prob-lem in Hilbert space.By incorporating the advantages of the stochastic approximation ap-proach and the alternating direction method of multipliers(ADMM),we propose a stochas-tic ADMM algorithm.This method decouples the stochasticity arising from the random equation constraint from the nonsmoothness of the control objective,allowing them to be tackled separately within the iterations.We introduce stochastic gradients and develop a proximal linearization technique for the stochastic subproblem,allowing each subprob-lem to admit a closed-form solution.The convergence and a high-probability bound of the proposed method are analyzed for the model problem.Numerical results demonstrate the effectiveness and efficiency of our method.
年，卷(期)：
2026, 44(6)
分类号：
90C15
62L20
35R60
60H35
机标分类号：
S
TP391.4
X591
在线出版日期：
2026年9月15日
