Journal of Convex Analysis 33 (2026), No. 1&2, 207--225
Copyright Heldermann Verlag 2026
Subgradient Evolution of Value Functions of Discrete-Time Convex Bolza Problems
Julio Deride
Universidad Adolfo Ibanez, Santiago, Chile
julio.deride@uai.cl
Cristopher Hermosilla
Universidad Técnica Federico Santa Maria, Valparaiso, Chile
cristopher.hermosill@usm.cl
Mattia Solla
Dept. of Industrial and Systems Engineering, University of Southern California, Los Angeles, U.S.A.
sollasae@usc.edu
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 method of characteristics 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 discuss about the qualification conditions required for our results, showing in particular that classical problems, such as the Linear Quadratic Regulator, satisfy these hypotheses.
Keywords: Optimal control, Discrete-time systems, Convex Bolza problems, Linear Quadratic Regulator, Mixed constraints.
MSC: 93C55, 46N10, 49N10, 49N15.
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