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Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control

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Listed:
  • Engel John C. Dela Vega

    (Imperial College)

  • Harry Zheng

    (Imperial College)

Abstract

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.

Suggested Citation

  • Engel John C. Dela Vega & Harry Zheng, 2023. "Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 80-111, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02237-w
    DOI: 10.1007/s10957-023-02237-w
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    References listed on IDEAS

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    1. Dongmei Zhu & Harry Zheng, 2022. "Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 191-219, July.
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