Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control

Engel John C. Dela Vega () and Harry Zheng ()
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Engel John C. Dela Vega: Imperial College
Harry Zheng: Imperial College

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 3, 80-111

Abstract: 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.

Keywords: Linear convex stochastic control; Random coefficients; Control constraints; Nondifferentiable objective function; Dual stochastic maximum principle; Primal–dual relation; 93E20; 49N05; 49N15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02237-w

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