196
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A trust region method with project step for bound constrained optimization without compact condition

&
Pages 449-460 | Received 27 Jul 2019, Accepted 05 Apr 2020, Published online: 26 Apr 2020

References

  • J. Barzilai, J.M. Borwein, Two point step size gradient methods. IMA J. Numer. Anal. 8 (1988), pp. 141–148. doi: 10.1093/imanum/8.1.141
  • S. Bellavia and B. Morini, Subspace trust-region methods for large bound-constrained nonlinear equations, SIAM J. Numer. Anal. 44 (2006), pp. 1535–1555. doi: 10.1137/040611951
  • S. Bellavia and S. Pieraccini, An affine scaling inexact dogleg methods for bound-constrained nonlinear systems, Optim. Methods. Soft. 30 (2015), pp. 276–300. doi: 10.1080/10556788.2014.955496
  • D.P. Bertsekas, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control. Optim. 20 (1982), pp. 221–246. doi: 10.1137/0320018
  • J.V. Burke, J.J. Moré, and G. Toraldo, Convergence properties of trust region methods for linear and convex constraints, Math. Program. 47 (1990), pp. 305–336. doi: 10.1007/BF01580867
  • R.H. Byrd, P. Lu, and J. Nocedal, A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Stat. Comput. 16 (1995), pp. 1190–1208. doi: 10.1137/0916069
  • T.F. Coleman and Y. Li, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim. 6 (1996), pp. 418–445. doi: 10.1137/0806023
  • J.E. Dennis and L.N. Vicente, Trust-region interior-point algorithms for minimization problems with simple bounds, in Applied mathematics and parallel computing, Festschrift for Klaus Ritter, H. Fischer, B. Riedmiller, and S. Schaffler, eds., Physica, Heidelberg, 1996, pp. 97–107.
  • F. Facchinei, J. Júdice, and J. Soares, An active set Newton algorithm for large-scale nonlinear programs with box constraints, SIAM J. Optim. 8 (1998), pp. 158–186. doi: 10.1137/S1052623493253991
  • R. Fletcher, Practical Methods of Optimization, 2nd ed., Vol. 2, Wiley and Sons, New York, 1980.
  • E.M. Gertz, A quasi-Newton trust-region method, Math. Program, Ser. A 100 (2004), pp. 447–470.
  • W.W. Hager, Minimizing a quadratic over a sphere, SIAM J. Optim. 12 (2001), pp. 188–208. doi: 10.1137/S1052623499356071
  • W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer, Berlin, 1980.
  • C. Kanzow, An active set-type Newton method for constrained nonlinear systems, in M.C. Ferris, O.L. Mangasarian, J.-S. Pang, eds., Complementarity: Applications, Algorithms and Extensions, Kluwer Academic, Dordrecht, 2001, pp. 179–200.
  • C. Kanzow and A. Klug, On affine-scaling interior-point Newton methods for nonlinear minimization with bound constraints, Comput. Optim. Appl. 35 (2006), pp. 177–197. doi: 10.1007/s10589-006-6514-5
  • C. Kanzow and A. Klug, An interior-point affine-scaling trust-region method for semismooth equations with box constraints, Comput. Optim. Appl. 37 (2007), pp. 329–353. doi: 10.1007/s10589-007-9029-9
  • D. Karaboga and B. Akay, A comparative study of artifical Bee colony algorithm, Appl. Math. Comput.214 (2009), pp. 108–132.
  • D.C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Prog. 45 (1989), pp. 503–528. doi: 10.1007/BF01589116
  • J.J. Moré, Trust regions and projected gradients, in Systems Modelling and Optimization: Proceedings of the 13th 1FIP Conference on System Modelling and Optimization, M. Iri and K. Yajima, eds., August 31–September 4, 1987 Tokyo, Japan: Lecture Notes in Control and Information Sciences, Vol. 113, Springer, Berlin, 1988, pp. 1–13.
  • L. Qi, X. Tong, and D. Li, Active set projected trust region algorithm for box constrained nonsmooth equations, J. Optim. Theory. Appl. 120 (2004), pp. 601–625. doi: 10.1023/B:JOTA.0000025712.43243.eb
  • K. Schittkowski, More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 282, Springer, Berlin, 1987.
  • L.K. Schubert, Modification of a quasi-Newton method for nonlinear equations with sparse Jacobian, Math. Comput. 24 (1970), pp. 27–30. doi: 10.1090/S0025-5718-1970-0258276-9
  • M.V. Solodov and B.F. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, in Reformulation: Piecewise Smooth, Semi-smooth and Smoothing Methods, M. Fukushima, and L. Qi, eds., Kluwer, Dordrecht, 1998, pp. 355–369.
  • X.J. Tong and L. Qi, On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions, J. Optim. Theory. Appl. 123 (2004), pp. 187–211. doi: 10.1023/B:JOTA.0000043997.42194.dc
  • Ph.L. Toint, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, Academic Press, New York, 1981, pp. 57–87.
  • M. Ulbrich, Non monotone trust-region methods for bound-constrained semismooth equations with applications to nonlinear mixed complementarity problems, SIAM J. Optim. 11 (2001), pp. 889–917. doi: 10.1137/S1052623499356344
  • Z.H. Wang and Y. Yuan, A subspace implementation of quasi-Newton trust-region methods for unconstrained optimization, Numer. Math. 104 (2006), pp. 241–269. doi: 10.1007/s00211-006-0021-6
  • Q.Y. Zhou, W.Y. Sun, and H.C. Zhang, A new trust region method with simple model for large scale optimization, Sci. China 59 (2016), pp. 2265–2280. doi: 10.1007/s11425-015-0734-2

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.