Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 80, 2003 - Issue 2
Submit an article Journal homepage
30
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Solution Of Bounded Nonlinear Systems Of Equations Using Homotopies With Inexact Restoration

E. G. Birgin Department of Computer Science IME-USP, University of São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, 05508-900, SP, Brazil
,
N. KrejiĆ Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000, Yugoslavia
&
J. M. MartÍnez Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, Campinas, 13081-970, SP, Brazil
Pages 211-222 | Published online: 15 Sep 2010

  • Abadie , J. and Carpentier , J. 1968 . “ Generalization of the Wolfe reduced-gradient method to the case of nonlinear constraints ” . In Optimization , Edited by: Fletcher , R. 37 – 47 . New York : Academic Press .
  • Allgower , E. and Georg , K. 1980 . Simplicial and continuation methods for approximating fixed points and solutions to systems of equations . SIAM Review , 22 : 28 – 85 .
  • Allgower , E. and Georg , K. 1989 . Estimates for piecewise linear approximations of implicitly defined manifolds . Applied Mathematics Letters , S : 1 – 7 .
  • Allgower , E. and Georg , K. 1990 . Numerical continuation methods: an introduction , Series in Computational Mathematics 13 Berlin : Springer .
  • Allgower , E. and Georg , K. 1997 . “ Numerical path following ” . In Handbook of Numerical Analysis , Edited by: Ciarlet , P. G. and Lions , J. L. Vol. 5 , 3 – 207 . Amsterdam : North Holland .
  • Friedlander , A. , Gomes-Ruggiero , M A. , Kozakevich , D. N. , Martinez , J. M and Santos , S. A. 1997 . Solving nonlinear systems of equations by means of quasi-Newton methods with a nonmonotone strategy . Optimization Methods and Software , 8 : 25 – 51 .
  • Gomes , F. A. M. , Maciel , M. C. and Matíhez , J. M. 1999 . Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters . Mathematical Programming , 84 : 161 – 200 .
  • Lasdon , L. S. 1982 . “ Reduced Gradient Methods ” . In Nonlinear Optimization 1981 , Edited by: Powell , M. J. D. 235 – 242 . New York : Academic Press .
  • Martinez , J. M. 1998 . Two-phase model algorithm with global convergence for nonlinear programming . Journal of Optimization Theory and Applications , 96 : 397 – 436 .
  • Martinez , J. M. 2001 . Inexact-restoration methods with Lagrangian tangent decrease and a new merit function for nonlinear programming . Journal of Optimization Theory and Applications , 111 : 39 – 58 .
  • Martinez , J. M. and Pilotta , E. A. 2000 . Inexact-restoration algorithm for constrained optimization . Journal of Optimization Theory and Applications , 104 : 135 – 163 .
  • Miele , A. , Huang , H. Y. and Heideman , J. C. 1969 . Sequential gradient-restoration algorithm for the minimization of constrained functions, ordinary and conjugate gradient version . Journal of Optimization Theory and Applications , 4 : 213 – 246 .
  • Miele , A. , Levy , A. V and Cragg , E. E. 1971 . Modifications and extensions of the conjugate-gradient restoration algorithm for mathematical programming problems . Journal of Optimization Theory and Applications , 7 : 450 – 472 .
  • Paloschi , J. R. 1995 . Bounded homotopies to solve systems of algebraic nonlinear equations . Computers and Chemical Engineering , 19 : 1243 – 1254 .
  • Paloschi , J. R. 1997 . Bounded homotopies to solve systems of sparse of algebraic nonlinear equations . Computers and Chemical Engineering , 21 : 531 – 541 .
  • Paloschi , J. R. 1998 . Using sparse bounded homotopies in the SPEEDUP simulation package . Computers and Chemical Engineering , 9 : 1181 – 1187 .
  • Rheinboldt , W. C. 2000 . Numerical continuation methods: a perspective . Journal of Computational and Applied Mathematics , 124 : 229 – 244 .
  • Rheinboldt , W. C. and Burkardt , J. V. 1983 . A locally parametrized continuation process . ACM Transactions on Mathematical Software , 9 : 215 – 235 .
  • Rosen , J. B. 1960 . The gradient projection method for nonlinear programming, part 1, linear constraints . SlAM Journal on Applied Mathematics , 8 : 181 – 217 .
  • Rosen , J. B. 1961 . The gradient projection method for nonlinear programming, part 2, nonlinear constraints . SIAM Journal on Applied Mathematics , 9 : 514 – 532 .
  • Seader , J. D. , Kuno , M. , Lin , W. , Johnson , S. , Unsworth , K. and Wiskin , J. 1990 . Mapped continuation methods for computing all solutions to general systems of nonlinear equations . Computers and Chemical Engineering , 14 : 71 – 85 .
  • Tanskanen , J. and Pohjola , V J. 2000 . A robust method for predicting state profiles in a reactive distillation . Computers and Chemical Engineering , 24 : 81 – 88 .
  • Tanskanen , J. and Pohjola , V. J. 2000 . Minimum internal recycle in nonideal homogeneous multicomponent distillation . Chemical Engineering Science , 55 : 2713 – 2726 .
  • Watson , L. T. , Billups , S. C. and Morgan , A. P. 1987 . Algorithm 652 HOMPACK: A suite of codes for globally convergent homotopy algorithms . ACM Transactions on Mathematical Software , 13 : 281 – 310 .
  • Watson , L. T. , Sosonkina , M. , Melville , R. C. , Morgan , A. P. and Walker , H. F. 1997 . Algorithm 777. HOMPACK90: A suite of Fortran 90 codes for globally convergent homotopy algorithms . ACM Transactions on Mathematical Software , 23 : 514 – 549 .

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.