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arXiv · 2402.00289

Subgradient evolution of value functions in discrete-time optimal control

Julio Deride·Cristopher Hermosilla·Mattia Solla
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Abstract

In this paper we investigate how the subgradients of the value function of a discrete-time convex Bolza problem evolve over time. In particular, we develop a discrete-time version of the characteristic method introduced by Rockafellar and Wolenski in the 2000s, by showing that the time-evolution of the subgradients of the value functions can be associated with trajectories of a discrete-time Hamiltonian system. To do so, we first prove that the value function has a dual counterpart, which corresponds to the conjugate of the value function of a suitable dual problem. We finally make a discussion about the qualification conditions we require for our results, showing in particular that classical problems, such as the Liner-Quadratic regulator, satisfy these hypotheses.

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Julio Deride, Cristopher Hermosilla, Mattia Solla. 2024-02-01. Subgradient evolution of value functions in discrete-time optimal control. https://arxiv.org/abs/2402.00289

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