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Original Articles

A Trust Region Algorithm with Memory for Equality Constrained Optimization

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Pages 717-734 | Published online: 04 Jun 2008

REFERENCES

  • E.S. Bothina ( 2003 ). A global convergence theory for an active-trust-region algorithm for solving the general nonlinear programming problem . Appl. Math. Computat. 144 : 127 – 157 .
  • R.H. Byrd , R.B. Schnabel , and G.A. Schultz ( 1987 ). A trust region algorithm for nonlinearly constrained optimization . SIAM J. Numer. Anal. 24 : 1152 – 1169 .
  • A.R. Conn , N.I.M. Gould , and P.L. Toint ( 2000 ). Trust Region Methods , MSP-SIAM Series on Optimization . Philadelphia , PA .
  • Y.H. Dai ( 2002 ). On the nonmonotone line search . J. Optim. Theory Appl. 112 : 315 – 330 .
  • J.E. Dennis , M.M. El-Alem , and M.C. Maciel ( 1997 ). A global convergence theory for general trust region-based algorithms for equality constrained optimization . SIAM J. Optim. 7 : 177 – 207 .
  • J.E. Dennis and L.N. Vicente ( 1997 ). On the convergence theory of trust-region-based algorithms for equality constrained optimization . SIAM J. Optim. 7 : 927 – 950 .
  • N.Y. Deng , Y. Xiao , and F. Zhou ( 1993 ). Nonmonotone trust region algorithm . J. Optim. Theory Appl. 76 : 259 – 285 .
  • M. EL-Alem ( 1999 ). A global convergence theory for Dennis. EL-Alem and Maciel's class of trust region algorithms for constrained optimization without assuming regularity . SIAM J. Optim. 9 : 965 – 990 .
  • M. EL-Alem ( 1995 ). Global convergence without the assumption of linear independence for a trust region algorithm for constrained optimization . J. Optim. Theory Appl. 87 : 563 – 577 .
  • N.I.M. Gould , S. Lucidi , M. Roma , and P.L. Toint ( 1998 ). A line search algorithm with memory for unconstrained optimization . In: High Performance Algorithms and Software in Nonlinear Optimization ( Deleone , Mauli , Pardalos , and Toraldo , eds.), Kluwer Academic Publishers , Dordrecht , pp. 207 – 223 .
  • L. Grippo , F. Lampariello , and S. Lucidi ( 1986 ). A nonmonotone line search technique for Newton's method . SIAM J. Numer. Anal. 23 : 707 – 716 .
  • E.O. Omojokun ( 1989 ). Trust Region Algorithm for Optimization with Equalities and Inequalities Constraints . Ph.D thesis, University of Corolado at Boulder .
  • E.R. Panier and A.L. Tits ( 1991 ). Avoiding Maratos effect by means of nonmonotone line search constrained problems . SIAM J. Numer. Anal. 28 : 1183 – 1190 .
  • M.J.D. Powell ( 1984 ). On global convergence of trust region algorithms for unconstrained optimization . Math. Programming 29 : 297 – 303 .
  • M.J.D. Powell and Y. Yuan ( 1991 ). A trust region algorithm for equality constrained optimization . Math. Programming 49 : 189 – 211 .
  • W.Y. Sun , J.Y. Han , and J. Sun ( 2002 ). Global convergence of non-monotone descent methods for unconstrained optimization problems . J. Computat. Appl. Math. 146 : 89 – 98 .
  • P.L. Toint ( 1997 ). A nonmonotone trust region algorithm for nonlinear programming subject to convex constraints . Math. Programming 77 : 69 – 94 .
  • P.L. Toint ( 1996 ). An assessment of nonmonotone line search technique for unconstrained optimization . SIAM J. Sci. Comput. 17 : 725 – 739 .
  • M. Ulbrich ( 2001 ). Nonmonotone trust region methods for bound-constrained semi-smooth equation with application to nonlinear mixed complementarity problems . SIAM J. Optim. 11 :889-917.
  • A. Vardi ( 1985 ). A trust region algorithm for equality constrained minimization: convergence properties and implemention . SIAM J. Numer. Anal. 22 : 575 – 591 .
  • J.L. Zhang ( 2001 ). Trust Region Algorithm for Nonlinear Optimization . Ph.D thesis, Institute of Applied Mathematics, Chinese Academy of Science .

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