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Original Articles

An Affine Scaling Interior Trust-Region Algorithm Combining Backtracking Line Search with Filter Technique for Nonlinear Constrained Optimization

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Pages 1046-1066 | Received 27 Apr 2014, Accepted 17 Apr 2015, Published online: 27 Jul 2015

REFERENCES

  • Z. Chen ( 2006 ). A penalty-free-type nonmonotone trust-region method for nonlinear constrained optimization . Appl. Math. Comput. 173 : 1014 – 1046 .
  • R. Fletcher and S. Leyffer ( 2002 ). Nonlinear programming without a penalty function . Math. Program. 91 : 239 – 269 .
  • R. Fletcher , S. Leyffer , and P. L. Toint ( 2002 ). On the global convergence of a filter-SQP algorithm . SIAM J. Optim. 13 : 44 – 59 .
  • N. I. M. Gould , Y. Loh , and D. P. Robinson ( 2014 ). A filter method with unified step computation for nonlinear optimization . SIAM J. Optim. 24 : 175 – 209 .
  • C. Gu and D. Zhu ( 2011 ). A secant algorithm with line search filter method for nonlinear optimization . Appl. Math. Model. 35 : 879 – 894 .
  • W. Hock and K. Schittkowski ( 1981 ). Test examples for nonlinear programming codes . Lecture Notes in Economics and Mathematics System , Vol. 187 . Springer-Verlag , Berlin .
  • M. Lalee , J. Nocedal , and T. D. Plantenga ( 1998 ). On the implementation of an algorithm for large-scale equality constrained optimization . SIAM J. Optim. 8 : 682 – 706 .
  • J. Nocedal and S. Wright ( 1999 ). Numerical Optimization . Springer-Verlag , New York .
  • M. J. D. Powell and Y. Yuan ( 1991 ). A trust-region algorithm for equality constrained optimization . Math. Program. 49 : 189 – 211 .
  • K. Schittkowski ( 1987 ). More test examples for nonlinear mathematical programming codes . Lecture Notes in Economics and Mathematics System , Vol. 282 . Springer-Verlag , Berlin .
  • C. Shen , S. Leyffer , and R. Fletcher ( 2012 ). A nonmonotone filter method for nonlinear optimization . Comput. Optim. Appl. 52 : 583 – 607 .
  • K. Su and H. An ( 2012 ). Global convergence of a nonmonotone filter method for equality constrained optimization . Appl. Math. Comput. 218 : 9396 – 9404 .
  • K. Su and D. Pu ( 2009 ). A nonmonotone filter trust region method for nonlinear constrained optimization . J. Comput. Appl. Math. 223 : 230 – 239 .
  • M. Ulbrich , S. Ulbrich , and L. N. Vicente ( 2004 ). A globally convergent primal-dual interior-point filter method for nonlinear programming . Math. Program. Ser. A. 100 : 379 – 410 .
  • S. Ulbrich ( 2004 ). On the superlinear local convergence of a filter-SQP method . Math. Program. Ser. B. 100 : 217 – 245 .
  • L. N. Vicente ( 2000 ). Local convergence of the affine-scaling interior-point algorithm for nonlinear programming . Comput. Optim. Appl. 17 : 23 – 35 .
  • A. Wächter and L. T. Biegler ( 2005 ). Line search filter methods for nonlinear programming: motivation and global convergence . SIAM J. Comput. 16 : 1 – 31 .
  • H. Wang and D. Pu ( 2013 ). A nonmonotone filter trust region method for the system of nonlinear equations . Appl. Math. Model. 37 : 498 – 506 .
  • Z. Yang and W. Sun ( 2008 ). A filter-trust-region method for LC1 unconstrained optimization and its global convergence . Analysis in Theory and Applications 24 ( 1 ): 55 – 66 .
  • X. Zhang , Z. Liu , and S. Liu ( 2012 ). A trust region SQP-filter method for nonlinear second-order cone programming . Comput. Math. Appl. 63 : 1569 – 1576 .
  • D. Zhu ( 2005 ). Projected reduced Hessian algorithm with affine scaling interior point for nonlinear constrained optimization . Chinese J. Contemp. Math. 26 : 227 – 248 .
  • D. Zhu ( 2005 ). An affine scaling projective reduced Hessian algorithm for minimum optimization with nonlinear equality and linear inequality constraints . Appl. Math. Comput. 166 : 131 – 163 .

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