Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control
Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control
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DOI：
10.1007/s10957-023-02237-w
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发表时间：
2023-07
影响因子：
1.9
通讯作者：
Engel John C. Dela Vega;Harry Zheng
中科院分区：
文献类型：
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作者：
Engel John C. Dela Vega;Harry Zheng
本文讨论了具有不可微目标函数、控制约束和随机系数的一般多维线性凸随机控制问题。我们制定了一个等价的对偶问题，证明了对偶随机最大值原理和原始和对偶问题之间的最优控制，最优状态和伴随过程的关系，并说明了一些例子的对偶方法的有用性。
In this paper, we discuss a general multidimensional linear convex stochastic control problem with nondifferentiable objective function, control constraints, and random coefficients. We formulate an equivalent dual problem, prove the dual stochastic maximum principle and the relation of the optimal control, optimal state, and adjoint processes between primal and dual problems, and illustrate the usefulness of the dual approach with some examples.