165
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A new inertial projected reflected gradient method with application to optimal control problems

&
Pages 197-226 | Received 18 Dec 2021, Accepted 04 Aug 2023, Published online: 15 Aug 2023

References

  • W. Alt, R. Baier, M. Gerdts, and F. Lempio, Error bounds for euler approximation of linear-quadratic control problems with bang-bang solutions, Numer. Algebra Control Optim. 2(3) (2012), pp. 547–570.
  • C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities; Applications to Free Boundary Problems, Wiley, New York, 1984.
  • H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, Springer, New York, 2011.
  • A. Bressan and B. Piccoli, Introduction to the Mathematical Theory of Control, AIMS Series on Applied Mathematics, Springfield, 2007.
  • Y. Censor, A. Gibali, and S. Reich, The subgradient extragradient method for solving variational inequalities in Hilbert space, J. Optim. Theory Appl. 148(2) (2011), pp. 318–335.
  • Y. Censor, A. Gibali, and S. Reich, Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space, Optim. Meth Softw. 26(4-5) (2011), pp. 827–845.
  • Y. Censor, A. Gibali, and S. Reich, Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space, Optimization 61(9) (2012), pp. 1119–1132.
  • X. Chang, S. Liu, Z. Deng, and S. Li, An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems, Optim. Meth. Soft. 37(4) (2022), pp. 1507–1526.
  • Q.L. Dong, S. He, and L. Liu, A general inertial projected gradient method for variational inequality problems, Comp. Appl. Math. 40(5) (2021), pp. 168.
  • P.T. Harker and J.-S. Pang, A damped-Newton method for the linear complementarity problem, in Computational Solution of Nonlinear Systems of Equations, Lectures in Appl. Math. 26, G. Allgower and K. Georg, eds., AMS, Providence, RI, 1990, pp. 265–284.
  • D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
  • G.M. Korpelevich, The extragradient method for finding saddle points and other problems, Ekonomika I Mat. Metody 12 (1976), pp. 747–756.
  • P.-E. Maingé, Numerical approach to monotone variational inequalities by a one-step projected reflected gradient method with line-search procedure, Comp. Math. Appl. 72(3) (2016), pp. 720–728.
  • P.-E. Maingé and M.L. Gobinddass, Convergence of one-step projected gradient methods for variational inequalities, J. Optim. Theory Appl. 171(1) (2016), pp. 146–168.
  • Y. Malitsky, Golden ratio algorithms for variational inequalities, Math. Program. 184(1-2) (2020), pp. 383–410.
  • Y.V. Malitsky, Projected reflected gradient methods for monotone variational inequalities, SIAM J. Optim. 25(1) (2015), pp. 502–520.
  • D.V. Thong, A. Gibali, and P.T. Vuong, An explicit algorithm for solving monotone variational inequalities, Appl. Numer. Math. 171 (2022), pp. 408–425.
  • A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1999.
  • A. Pietrus, T. Scarinci, and V.M. Veliov, High order discrete approximations to Mayer's problems for linear systems, SIAM J. Control Optim. 56(1) (2018), pp. 102–119.
  • L.D. Popov, A modification of the Arrow-Hurwicz method for finding saddle points, Math. Notes 28(5) (1980), pp. 845–848.
  • J. Preininger and P.T. Vuong, On the convergence of the gradient projection method for convex optimal control problems with bang-bang solutions, Comput. Optim. Appl. 70(1) (2018), pp. 221–238.
  • W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.
  • P. Tseng, A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Optim. 38(2) (2000), pp. 431–446.
  • D.V. Thong, X.H. Li, Q.L. Dong, Y.J. Cho, and T.M. Rassias, An inertial Popov's method for solving pseudomonotone variational inequalities, Optim. Lett. 15(2) (2021), pp. 757–777.
  • J. Yang and H. Liu, A modified projected gradient method for monotone variational inequalities, J. Optim. Theory Appl. 179(1) (2018), pp. 197–211.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.