Hubert Halkin

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 Kelley-Bryson discrete costate recursion reduces to 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