139
Views
56
CrossRef citations to date
0
Altmetric
Review

An affine scaling interior trust-region method combining with nonmonotone line search filter technique for linear inequality constrained minimization

ORCID Icon &
Pages 1494-1526 | Received 20 Apr 2016, Accepted 30 Mar 2017, Published online: 27 May 2017

References

  • N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim. 10 (2008), pp. 147–161.
  • 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
  • T.F. Coleman and Y. Li, A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints, Math. Program. Ser. A 88 (2000), pp. 1–31. doi: 10.1007/PL00011369
  • A.R. Conn, N.I.M. Gould and P.L. Toint, Testing a class of methods for solving minimization problems with simple bounds on the variables, Math. Comput. 50 (1988), pp. 399–430. doi: 10.1090/S0025-5718-1988-0929544-3
  • N.Y. Deng, Y. Xiao and F.J. Zhou, Nonmonotonic trust region algorithm, J. Optim. Theory Appl. 76 (1993), pp. 259–285. doi: 10.1007/BF00939608
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program 91 (2002), pp. 201–213. doi: 10.1007/s101070100263
  • R. Fletcher, Practical Methods of Optimization, Vol. I: Unconstrained Optimization; Vol. II: Constrained Optimization, Wiley, New York, 1980.
  • R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Program. 91 (2002), pp. 239–269. doi: 10.1007/s101070100244
  • N.I.M. Gould, C. Sainvitu and P.L. Toint, A filter-trust-region method for unconstrained optimization, SIAM J. Optim. 16 (2005), pp. 341–357. doi: 10.1137/040603851
  • L. Grippo, F. Lampariello and S. Lucidi, A nonmonotonic line search technique for Newton's methods, SIAM J. Numer. Anal. 23 (1986), pp. 707–716. doi: 10.1137/0723046
  • C. Gu and D. Zhu, A nonmonotone line search filter method with reduced Hessian updating for nonlinear optimization, J. Syst. Sci. Complex. 26 (2013), pp. 534–555. doi: 10.1007/s11424-012-0036-2
  • W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematics System, vol. 187, Springer-Verlag, Berlin, 1981.
  • J.J. Moré and D.C. Sorensen, Computing a trust region step, SIAM J. Sci. Stat. Comput. 4 (1983), pp. 553–572. doi: 10.1137/0904038
  • J. Nocedal and Y. Yuan, Combining trust region and line search techniques, in Advances in Nonlinear Programming, Y. Yuan, eds., Kluwer, Dordrecht, 1998, pp. 153–175.
  • J.-S. Pang and L. Qi, Nonsmooth equations: Motivation and algorithms, SIAM J. Optim. 3 (1993), pp. 443–465. doi: 10.1137/0803021
  • Y. Pei and D. Zhu, A trust-region algorithm combining line search filter technique for nonlinear constrained optimization, Int. J. Comput. Math. 8 (2014), pp. 1817–1839. doi: 10.1080/00207160.2013.863282
  • M.J.D. Powell, On the global convergence of trust region algorithms for unconstrained minimization, Math. Program. 29 (1984), pp. 297–303. doi: 10.1007/BF02591998
  • K. Schittkowski, More Test Examples for Nonlinear Mathematical Programming Codes, Lecture Notes in Economics and Mathematics System, vol. 282, Springer-Verlag, Berlin, 1987.
  • D.C. Sorensen, Newton's method with a model trust region modification, SIAM J. Numer. Anal. 19 (1982), pp. 409–426. doi: 10.1137/0719026
  • A. Wächter and L. Biegler, Line search filter methods for nonlinear programming: Motivation and global convergence, SIAM J. Comput. 16 (2005), pp. 1–31.
  • A. Wächter and L.T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim. 6 (2005), pp. 32–48. doi: 10.1137/S1052623403426544
  • Z. Wang and D. Zhu, An affine scaling interior point filter line-search algorithm for linear inequality constrained minimization, Numer. Funct. Anal. Optim. 31 (2010), pp. 955–973. doi: 10.1080/01630563.2010.496302
  • P. Wang and D. Zhu, An affine-scaling derivative-free trust-region method for solving nonlinear systems subject to linear inequality constraints, Int. J. Comput. Math. 92 (2015), pp. 1660–1687. doi: 10.1080/00207160.2014.959942
  • D. Zhu, A new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints, J. Comput. Appl. Math. 161 (2003), pp. 1–25. doi: 10.1016/S0377-0427(03)00458-8
  • D. Zhu, Nonmonotonic back-tracking trust region interior point algorithm for linear constrained optimization, J. Comput. Appl. Math. 155 (2003), pp. 285–305. doi: 10.1016/S0377-0427(02)00870-1
  • D.-T. Zhu, Superlinear convergence of affine scaling interior point Newton method for linear inequality constrained minimization without strict complementarity, Acta Math. Appl. Sin. 25 (2009), pp. 183–194. doi: 10.1007/s10255-007-7029-2

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.