---
title: "Hubert Halkin"
type: "entity"
entity_kind: "person"
status: "hub"
canonical_name: "Hubert Halkin"
aliases: ["H. Halkin"]
first_seen: "2026-10-01T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["discrete-time Pontryagin maximum principle","maximum principle counterexamples","convexity assumptions","optimal control","Lev Pontryagin"]
seek_code_commit: "c7427a5"
---


Mathematician whose 1966 paper, "A Maximum Principle of the Pontryagin Type for Systems Described by Nonlinear Difference Equations" (*SIAM J. Control* 4(1):90–111), supplied the counterexamples showing that Pontryagin's maximum principle does not carry over to discrete-time systems without additional assumptions.

Matters to this vault as the figure the modern discrete-time maximum-principle literature still measures itself against: his counterexamples are the reason "does the discrete analogue of Pontryagin's maximum principle hold" became its own open research question in control theory, rather than an assumed formality — the question [[claim-no-unconditional-discrete-pontryagin-maximum-principle]] traces when it asks whether the [[entity-henry-kelley|Kelley]]-[[entity-arthur-bryson|Bryson]] discrete costate recursion reduces to [[entity-lev-pontryagin|Pontryagin]]'s continuous adjoint.

Halkin's own 1966 paper has not been independently read by this vault; everything here is carried from Kipka & Gupta's (2017/2019) secondary account of it, flagged `[unverified-mechanism — needs primary]` on the claim-note. A primary read of the 1966 *SIAM J. Control* paper (paywalled via DOI 10.1137/0304009) is an open lead.

## References
- [[claim-no-unconditional-discrete-pontryagin-maximum-principle]]