Email this article On the Hamilton–Jacobi theory for nonsmooth variational problems
- Authors: Ioffe A.D.1
-
Affiliations:
- Technion – Israel Institute of Technology, Haifa, Israel
- Issue: Vol 216, No 3 (2025)
- Pages: 96-107
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/306688
- DOI: https://doi.org/10.4213/sm10239
- ID: 306688
Cite item
Open Access
Access granted
Subscription Access
Abstract
We consider the classical Bolza problem under fairly general assumptions on its components (the integrand and off-integral function).The main results obtained are: conditions for the semicontinuity of the value functions, a characterization of the subdifferential of the value function and a partial conversion of the latter result.Bibliography: 15 titles.
About the authors
Alexander Davidovich Ioffe
Technion – Israel Institute of Technology, Haifa, Israel
Email: ioffe@technion.ac.il
References
- P. Bettiol, R. B. Vinter, Principles of dynamic optimization, Springer Monogr. Math., Springer, Cham, 2024, xviii+781 pp.
- N. Bogoliouboff, “Sur quelques methodes nouvelles dans le calcul des variations”, Ann. Math. Pura Appl. (4), 7 (1930), 249–271
- A. D. Ioffe, “On lower semicontinuity of integral functionals. I”, SIAM J. Control Optim., 15:4 (1977), 521–538
- A. Ioffe, “Existence and relaxation theorems for unbounded differential inclusions”, J. Convex Anal., 13:2 (2006), 353–362
- A. D. Ioffe, Variational analysis of regular mappings. Theory and applications, Springer Monogr. Math., Springer, Cham, 2017, xxi+495 pp.
- A. D. Ioffe, “Maximum principles for optimal control problems with differential inclusions”, SIAM J. Control Optim., 62:1 (2024), 271–296
- А. Д. Иоффе, В. М. Тихомиров, Теория экстремальных задач, Наука, М., 1974, 479 с.
- F. H. Clarke, “The generalized problem of Bolza”, SIAM J. Control Optim., 14:4 (1976), 682–699
- P. D. Loewen, R. T. Rockafellar, “Optimal control of unbounded differential inclusions”, SIAM J. Control Optim., 32:2 (1994), 442–470
- C. Olech, “Weak lower semicontinuity of integral functionals”, J. Optim. Theory Appl., 19:1 (1976), 3–16
- J.-P. Penot, Calculus without derivatives, Grad. Texts in Math., 266, Springer, New York, 2013, xx+524 pp.
- R. T. Rockafellar, “Existence and duality theorems for convex problems of Bolza”, Trans. Amer. Math. Soc., 159 (1971), 1–40
- R. T. Rockafellar, “Existence theorems for general control problems of Bolza and Lagrange”, Adv. Math., 15:3 (1975), 312–333
- R. T. Rockafeller, R. J. B. Wets, Variational analysis, Grundlehren Math. Wiss., 317, Springer-Verlag, Berlin, 1998, xiv+733 pp.
- R. B. Vinter, Optimal control, Systems Control Found. Appl., Birkhäuser Boston, Inc., Boston, MA, 2000, xviii+507 pp.
Supplementary files
