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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 18 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 18
Number of page(s) 33
DOI https://doi.org/10.1051/cocv/2024004
Published online 07 March 2024
  1. H.M. Amman and D.A. Kendrick, Computing the steady state of linear quadratic optimization models with rational expectations. Econ. Lett. 58 (1998) 185–191. [Google Scholar]
  2. R.S. Burachik, C.Y. Kaya and S.N. Majeed, A duality approach for solving control-constrained linear-quadratic optimal control problems. SIAM J. Control Optim. 52 (2014) 1771–1782. [Google Scholar]
  3. C. Büskens and H. Maurer, SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control. J. Comput. Appl. Math. 120 (2000) 85–108. [Google Scholar]
  4. B. Christiansen, H. Maurer and O. Zirn, Optimal control of machine tool manipulators, in edited by M. Diehl, Recent Advances in Optimization and its Applications in Engineering. Springer-Verlag, Berlin, Heidelberg (2010) 451–460. [CrossRef] [Google Scholar]
  5. B. Kugelmann and H.J. Pesch, New general guidance method in constrained optimal control. I. Numerical method. J. Optim. Theory Appl. 67 (1990) 421–435. [Google Scholar]
  6. H. Maurer and H.J. Oberle, Second order sufficient conditions for optimal control problems with free final time: The Riccati approach. SIAM J. Control Optim. 41 (2003) 380–403. [Google Scholar]
  7. T. Mouktonglang, Innate immune response via perturbed LQ-control problem. Adv. Stud. Biol. 3 (2011) 327–332. [Google Scholar]
  8. M. Athans and P. Falb, Optimal Control: An Introduction to the Theory and Its Applications. McGraw-Hill, Inc., New York (1966). [Google Scholar]
  9. D.E. Kirk, Optimal Control Theory: An Introduction. Prentice-Hall, Inc., New Jersey (1970). [Google Scholar]
  10. J. Klamka, Controllability and Minimum Energy Control. Springer, Cham, Switzerland (2019). [CrossRef] [Google Scholar]
  11. S.P. Sethi, Optimal Control Theory: Applications to Management Science and Economics, 1st edn. Springer, Cham, Switzerland (2019). [CrossRef] [Google Scholar]
  12. H.H. Bauschke and V.R. Koch, Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation problems with Halfspaces. Infinite Products of Operators and Their Applications (2012) 1–40. [Google Scholar]
  13. F.J. Aragón Artacho, J.M. Borwein and M.K. Tam, Douglas–Rachford feasibility methods for matrix completion problems. ANZIAM J. 55 (2014) 299–326. [MathSciNet] [Google Scholar]
  14. S. Gravel and V. Elser, Divide and concur: a general approach to constraint satisfaction. Phys. Rev. E 78 (2008) 036706. [CrossRef] [PubMed] [Google Scholar]
  15. H.H. Bauschke, 8 Queens, Sudoku, and Projection Methods. https://carma.newcastle.edu.au/resources/jon/Preprints/Books/CUP/Material/Lions-Mercier/Heinz_Bauschke.pdf, 2008. [Google Scholar]
  16. F.J. Aragón Artacho, R. Campoy and V. Elser, An enhanced formulation for solving graph coloring problems with the Douglas–Rachford algorithm. J. Glob. Optim. 77 (2020) 383–403. [CrossRef] [Google Scholar]
  17. Y. Censor, M.D. Altschuler and W.D. Powlis, On the use of Cimminos simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning. Inverse Probl. 4 (1988) 607–623. [CrossRef] [Google Scholar]
  18. B. O’Donoghue, G. Stathopoulos and S. Boyd, A splitting method for optimal control. IEEE Trans. Contr. Syst. Tech. 21 (2013) 2432–2442. [CrossRef] [Google Scholar]
  19. H.H. Bauschke, R.S. Burachik and C.Y. Kaya, Constraint splitting and projection methods for optimal control of double integrator, in Splitting Algorithms, Modern Operator Theory, and Applications. Springer (2019) 45–68. [CrossRef] [Google Scholar]
  20. R. Fourer, D.M. Gay and B.W. Kernighan, AMPL: A Modeling Language for Math. Progr., 2nd edn. Brooks/Cole Publishing Company/Cengage Learning (2003). [Google Scholar]
  21. A. Wachter and L.T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Progr. 106 (2006) 25–57. [CrossRef] [Google Scholar]
  22. V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko and L.S. Pontryagin, The Mathematical Theory of Optimal Processes. John Wiley & Sons, New York (1962). [Google Scholar]
  23. M.R. Hestenes, Calculus of Variations and Optimal Control Theory. John Wiley & Sons, New York (1966). [Google Scholar]
  24. R.B. Vinter, Optimal Control. Birkhäuser, Boston (2000). [Google Scholar]
  25. B.S. Mordukhovich, Variational Analysis and Generalized Differentiation II: Applications. Springer-Verlag, Berlin, Heidelberg (2006). [Google Scholar]
  26. F. Clarke, Functional Analysis, Calculus of Variations and Optimal Control. Springer-Verlag, London (2013). [CrossRef] [Google Scholar]
  27. W.J. Rugh, Linear System Theory, 2nd edn. Pearson (1995). [Google Scholar]
  28. R.L. Borrelli and C.S. Coleman, Differential Equations: A Modeling Perspective, 2nd edn. John Wiley and Sons (2004). [Google Scholar]
  29. H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. 2nd edn. Springer (2017). [CrossRef] [Google Scholar]
  30. J. Douglas and H.H. Rachford, On the numerical solution of heat conduction problems in two and three space variables. Trans. Am. Math. Soc. 82 (1956) 421–439. [CrossRef] [Google Scholar]
  31. P.-L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16 (1979) 964–979. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Eckstein and D.P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Progr., Ser. A 55 (1992) 293–318. [Google Scholar]
  33. B.F. Svaiter, On weak convergence of the Douglas-Rachford method. SIAM J. Control Optim,. 49 (2011) 280–287. [CrossRef] [Google Scholar]
  34. H.H. Bauschke and W.M. Moursi, On the Douglas–Rachford algorithm. Math. Program., Ser. A 164 (2017) 263–284. [CrossRef] [Google Scholar]
  35. M.M. Alves, J. Eckstein, M. Geremia and J.G. Melo, Relative-error inertial-relaxed inexact versions of Douglas–Rachford and ADMM splitting algorithms. Comput. Optim. Appl. 75 (2020) 389–422. [CrossRef] [MathSciNet] [Google Scholar]
  36. B.F. Svaiter, A weakly convergent fully inexact Douglas–Rachford method with relative error tolerance. ESAIM. Control Optim. Calc. Var. 25 (2019). [Google Scholar]
  37. M.M. Alves and M. Geremia, Iteration complexity of an inexact Douglas–Rachford method and of a Douglas–RachfordTsengs F–B four-operator splitting method for solving monotone inclusions. Numer. Algorithms 82 (2019) 263–295. [CrossRef] [MathSciNet] [Google Scholar]
  38. H.H. Bauschke and W.M. Moursi, On the Douglas–Rachford algorithm for solving possibly inconsistent optimization problems. Math. Oper. Res. https://doi.org/10.1287/moor.2022.1347. [Google Scholar]
  39. W.W. Hager, Runge–Kutta methods in optimal control and the transformed adjoint system. Numer. Math. 87 (2000) 247–282. [CrossRef] [MathSciNet] [Google Scholar]
  40. R.S. Burachik, B.I. Caldwell and C.Y. Kaya, Projection methods for control-constrained minimum-energy control problems. arXiv:2210.17279v1, https://arxiv.org/abs/2210.17279. [Google Scholar]
  41. H.H. Bauschke and J.M. Borwein, On projection algorithms for solving convex feasibility problems. SIAM Rev. 38 (1996) 367426. [CrossRef] [MathSciNet] [Google Scholar]
  42. J. von Neumann, On rings of operators. Reduction theory. Ann. Math. 50 (1949) 401–485. [CrossRef] [MathSciNet] [Google Scholar]
  43. J.P. Boyle and R.L. Dykstra, A method for finding projections onto the intersection of convex sets in Hilbert spaces, in Advances in Order Restricted Statistical Inference, Vol. 37 of Lecture Notes in Statistics. Springer (1986) 28–47. [Google Scholar]
  44. F.J. Aragón Artacho and R. Campoy, A new projection method for finding the closest point in the intersection of convex sets. Comput. Optim. Appl. 69 (2018) 99–132. [CrossRef] [MathSciNet] [Google Scholar]

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