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Original Article

A central path interior point method for nonlinear programming and its local convergence

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Pages 2471-2495 | Received 02 Jan 2017, Accepted 07 Oct 2017, Published online: 22 Nov 2017

References

  • C. Audet and J.E. Dennis Jr., A pattern search filter method for nonlinear programming without derivatives, SIAM J. Optim. 14 (2004), pp. 980–1010. doi: 10.1137/S105262340138983X
  • H.Y. Benson, R.J. Vanderbei, and D.F. Shanno, Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions, Comput. Optim. Appl. 23 (2002), pp. 257–272. doi: 10.1023/A:1020533003783
  • R.H. Bielschowsky and F.A.M. Gomes, Dynamic control of infeasibility in equality constrained optimization, SIAM J. Optim. 19 (2008), pp. 1299–1325. doi: 10.1137/070679557
  • R.H. Byrd, G. Liu, and J. Nocedal, On the local behavior of an interior point method for nonlinear programming, in Numerical Analysis, D. Griffiths and D. Higham, eds., Addison-Wesley Longman, Reading, MA, 1997, pp. 37–56.
  • C.M. Chin and R. Fletcher, On the global convergence of an SLP-filter algorithm that takes EQP steps, Math. Program. 96 (2003), pp. 161–177. Available at http://dx.doi.org/10.1007/s10107-003-0378-6.
  • F.E. Curtis and J. Nocedal, Flexible penalty functions for nonlinear constrained optimization, IMA J. Numer. Anal. 28 (2008), pp. 749–769. doi: 10.1093/imanum/drn003
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201–213. doi: 10.1007/s101070100263
  • A.S. El-Bakry, R.A. Tapia, T. Tsuchiya, and Y. Zhang, On the formulation and theory of the newton interior-point method for nonlinear programming, J. Optim. Theory Appl. 89 (1996), pp. 507–541. Available at http://dx.doi.org/10.1007/BF02275347.
  • R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Program. 91 (2002), pp. 239–269. doi: 10.1007/s101070100244
  • R. Fletcher, S. Leyffer, and Ph.L. Toint, On the global convergence of a filter–SQP algorithm, SIAM J. Optim. 13 (2002), pp. 44–59. doi: 10.1137/S105262340038081X
  • R. Fletcher, N.I.M. Gould, S. Leyffer, Ph.L. Toint, and A. Wächter, Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming, SIAM J. Optim. 13 (2002), pp. 635–659. doi: 10.1137/S1052623499357258
  • N.I.M. Gould and Ph.L. Toint, Nonlinear programming without a penalty function or a filter, Math. Program. 122 (2010), pp. 155–196. doi: 10.1007/s10107-008-0244-7
  • N.I.M. Gould, S. Leyffer, and Ph.L. Toint, A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares, SIAM J. Optim. 15 (2004), pp. 17–38. doi: 10.1137/S1052623403422637
  • W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Code, Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer-Verlag, Berlin, 1987.
  • HSL, A Collection of Fortran Codes for Large Scale Scientific Computation, 2011. Available at http://www.hsl.rl.ac.uk.
  • X.W. Liu and Y.X. Yuan, A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization, SIAM J. Optim. 21 (2011), pp. 545–571. doi: 10.1137/080739884
  • J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
  • S.Q. Qiu and Z.W. Chen, Global and local convergence of a class of penalty-free-type methods for nonlinear programming, Appl. Math. Model. 36 (2012), pp. 3201–3216. doi: 10.1016/j.apm.2011.10.009
  • S.Q. Qiu and Z.W. Chen, A new penalty-free-type algorithm based on trust region techniques, Appl. Math. Comput. 218 (2012), pp. 11089–11099.
  • R. Silva, M. Ulbrich, S. Ulbrich, and L.N. Vicente, A globally convergent primal–dual interior-point filter method for nonlinear programming: New filter optimality measures and computational results, Tech. Rep., Centro de Matemática da Universidade de Coimbra, 2008.
  • S. Ulbrich, On the superlinear local convergence of a filter-SQP method, Math. Program. 100 (2004), pp. 217–245.
  • M. Ulbrich and S. Ulbrich, Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. Program. 95 (2003), pp. 103–135. doi: 10.1007/s10107-002-0343-9
  • M. Ulbrich, S. Ulbrich, and L.N. Vicente, A globally convergent primal–dual interior-point filter method for nonlinear programming, Math. Program. 100 (2004), pp. 379–410. doi: 10.1007/s10107-003-0477-4
  • R.J. Vanderbei and D.F. Shanno, An interior-point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl. 13 (1999), pp. 231–252. doi: 10.1023/A:1008677427361
  • A. Wächter and L.T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim. 16 (2005), pp. 32–48. doi: 10.1137/S1052623403426544
  • A. Wächter and L.T. Biegler, Line search filter methods for nonlinear programming: Motivation and global convergence, SIAM J. Optim. 16 (2005), pp. 1–31 (electronic). doi: 10.1137/S1052623403426556
  • A. Wächter and L.T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program. 106 (2006), pp. 25–57. doi: 10.1007/s10107-004-0559-y
  • W.J. Xue, C.G. Shen, and D.G. Pu, A penalty-function-free line search SQP method for nonlinear programming, J. Comput. Appl. Math. 228 (2009), pp. 313–325. doi: 10.1016/j.cam.2008.09.031
  • H. Yamashita, H. Yabe, and T. Tanabe, A globally and superlinearly convergent primal–dual interior point trust region method for large scale constrained optimization, Math. Program. 102 (2005), pp. 111–151. doi: 10.1007/s10107-004-0508-9

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