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Section B

Structured symmetric rank-one method for unconstrained optimization

, &
Pages 2608-2617 | Received 02 Jul 2010, Accepted 15 Dec 2010, Published online: 25 May 2011

References

  • Andrei , N. 2008 . An unconstrained optimization test functions collection . Adv. Model. Optim. , 10 : 147 – 161 .
  • Bartholomew-Biggs , M. C. 1977 . The estimation of the Hessian matrix in nonlinear least squares problems with non-zero residuals . Math. Program. , 12 : 67 – 80 .
  • Bongartz , I. , Conn , A. R. , Gould , N. I.M. and Toint , Ph. L. 1995 . CUTE: Constrained and unconstrained testing environment . ACM Trans. Math. Software , 21 : 123 – 160 .
  • Byrd , R. H. , Khalfan , H. F. and Schnabel , R. B. 1993 . “ Analysis of a symmetric rank-one trust region method ” . USA : Department of Computer Science, University of Colorado at Boulder . Tech. Rep. CU-CS-657-93
  • Chen , L. H. , Deng , N. Y. and Zhang , J. Z. 2006 . A modified quasi-Newton method for structured optimization with partial information on the Hessian . Comput. Optim. Appl , 35 ( 1 ) : 5 – 18 .
  • Conn , A. R. , Gould , N. I.M. and Toint , Ph. 1991 . Convergence of quasi-Newton matrices generated by the symmetric rank one update . Math. Program. , 48 : 549 – 560 .
  • Davidon , W. C. 1975 . Optimally conditioned optimization algorithms without line search . Math. Program. , 9 : 1 – 30 .
  • Dennis , J. E. Jr. 1975 . “ A brief survey of convergence results for quasi-Newton methods ” . Ithaca, NY, USA : Cornell University . Technical Report
  • Dennis , J. E. Jr. and Schnabel , R. B. 1983 . Numerical Methods for Unconstrained Optimization and Nonlinear Equations , Englewood Cliffs, NJ : Prentice-Hall .
  • Dennis , J. E. Jr. and Walker , H. F. 1981 . Convergence theorems for least-change secant update methods . SIAM J. Numer. Anal. , 18 : 949 – 987 .
  • Dennis , J. E. Jr. and Wolkowicz , H. 1993 . Sizing and least change secant methods . SIAM J. Numer. Anal , 30 ( 5 ) : 1291 – 1313 .
  • Dolan , E. D. and Moré , J. J. 2002 . Benchmarking optimization software with performance profiles . Math. Program , 91 ( 2 ) : 201 – 203 .
  • Dennis , J. E. Jr. , Gay , D. M. and Welsch , R. E. 1981 . An adaptive nonlinear least-squares algorithm . ACM Trans. Math. Software , 7 : 348 – 368 .
  • Dennis , J. E. Jr. , Martinez , H. J. and Tapia , R. A. 1989 . Convergence theory for the structured BFGS secant method with an application to nonlinear least squares . J. Optim. Theory Appl. , 61 : 161 – 178 .
  • Engels , J. R. and Martinez , H. J. 1991 . Local and superlinear convergence for partially known quasi-Newton methods . SIAM J. Optim. , 1 : 42 – 56 .
  • Fletcher , R. 1987 . Practical Methods of Optimization , 2 , Chichester : Wiley .
  • Ip , C. M. and Todd , M. J. 1988 . Optimal conditioning and convergence in rank one quasi-Newton updates . SIAM J. Numer. Anal. , 25 : 206 – 221 .
  • Leong , W. J. and Hassan , M. A. 2009 . A restarting approach for the symmetric rank one update for unconstrained optimization . Comput. Optim. Appl , 42 ( 3 ) : 327 – 334 .
  • Moré , J. J. and Thuente , D. J. 1994 . Line search algorithms with guaranteed sufficient decrease . ACM Trans. Math. Software , 20 ( 3 ) : 286 – 307 .
  • Moré , J. J. , Garbow , B. S. and Hillstorm , K. E. 1981 . Testing unconstrained optimization software . ACM Trans. Math. Software , 7 ( 1 ) : 17 – 41 .
  • Shanno , D. F. and Phua , K. H. 1978 . Matrix conditioning and nonlinear optimization . Math. Program. , 14 : 149 – 160 .
  • Tapia , R. A. 1988 . On secant updates for use in general constrained optimization . Math. Comput. , 51 : 181 – 202 .
  • Wolkowicz , H. 1994 . Measure for symmetric rank-one updates . Math. Oper. Res , 19 ( 4 ) : 815 – 830 .
  • Yabe , H. and Takahashi , T. 1988 . Structured quasi-Newton methods for nonlinear least squares problems . TRU Math. , 24 : 195 – 209 .
  • Yabe , H. and Takahashi , T. 1991 . Factorized quasi-Newton methods for nonlinear least squares problems . Math. Program. , 51 ( 1–3 ) : 75 – 100 .
  • Yabe , H. and Yamaki , N. 1995 . Convergence of a factorized Broyden-like family for nonlinear least squares problems . SIAM J. Optim. , 5 : 770 – 791 .
  • Yabe , H. and Yamaki , N. 1996 . Local and superlinear convergence of structured quasi-Newton methods for nonlinear optimization . J. Oper. Res. Soc. Japan , 39 : 541 – 557 .

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