---
title: "William W. Hager"
type: "entity"
entity_kind: "person"
status: "hub"
canonical_name: "William W. Hager"
aliases: ["W. W. Hager"]
first_seen: "2026-10-01T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["Runge-Kutta methods","adjoint system consistency","optimal control","numerical analysis","Jerrold Marsden"]
seek_code_commit: "c7427a5"
---


Control theorist and numerical analyst at the University of Florida, known for consistency-and-convergence results relating Runge-Kutta discretizations of optimal-control problems to the corresponding continuous adjoint systems — including "Runge-Kutta methods in optimal control and the transformed adjoint system" (*Numerische Mathematik* 87:247–282, 2000) and a related 2001 convergence result with Dontchev and Veliov.

Matters to this vault as the technical backbone underneath the one rigorous proof this vault has found that the discrete costate recursion converges to [[entity-lev-pontryagin|Pontryagin]]'s continuous adjoint as step size → 0: Ober-Blöbaum, Junge & [[entity-jerrold-marsden|Marsden]]'s theorem explicitly builds on Hager's consistency-plus-stability framework ([[claim-ober-blobaum-junge-marsden-prove-discrete-adjoint-converges-to-continuous]]).

Hager's own papers have not been independently read by this vault — both are paywalled at Springer and only known via Ober-Blöbaum/Junge/Marsden's citation; his faculty page lists the 2000 paper without a direct PDF link. A primary read remains an open lead.

## References
- [[claim-ober-blobaum-junge-marsden-prove-discrete-adjoint-converges-to-continuous]]