Variants of the reduced Newton method for nonlinear equality constrained optimization problems

References

• Abadie , J. and Carpentier , J. 1969 . “ Generalization of the Wolfe Reduced Gradient method to the case of nonlinear constraints ” . In Optimization , Edited by: Fletcher , R. Academic Press .
   Google Scholar
• Brent , R.P. 1973 . Some efficient algorithms for solving systems of nonlinear equations . SIAM J. Numer. Anal , 10 : 327 – 344 .
   Web of Science ®Google Scholar
• Demo , R.S. 1982 . “ Large scale nonlinear optimization ” . In Nonlinear Optimization 1981 , Edited by: Powell , M.J. Academic Press .
   Google Scholar
• Fletcher R. Methods for nonlinear constraints ibid
   Google Scholar
• Gabay , D. and Luenberger , D.G. 1976 . Efficiently converging minimization methods based on the reduced gradient . SIAM J.Control and Optim , 14 ( 1 ) : 42 – 61 .
   Web of Science ®Google Scholar
• Gill , P.E. and Murray , W. 1974 . “ Newton-type methods for linearly constrained optimization ” . In Numerical Methods for Constrained Optimization , Edited by: Gill , P.E. and Murray , W. Academic Press .
   Google Scholar
• Hoyer , W. and Schmidt , J.W. 1984 . Newton-type decomposition methods for equations arising in network analysis . ZAMM , 64 : 397 – 405 .
   Web of Science ®Google Scholar
• Kleinmichel , H. 1984 . Private communication
   Google Scholar
• Lasdon , L.S. 1981 . “ Reduced gradient methods ” . In Nonlinear Optimization Edited by: Powell , M.J.D.
   Google Scholar
• Lasdon , L.S. and Waren , A.D. 1978 . “ Generalized reduced gradient software for linearly and nonlinearly constrained problems ” . In Design and Implementation of Optimization Software , Edited by: Greenberg , H.J. Sijthoff and Noordhoff, Alphen aan den Rijn .
   Google Scholar
• Menzel R. An effective algorithm for a class of equality-constrained optimization problems Submitted to optimization
   Google Scholar
• Ortega , J.M. and Rheintboldt , W.C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , Academic Press .
   Google Scholar
• Poljak , B.T. 1983 . Vvedenie v optimizaciju , Moskva : Nauka . Russ
   Google Scholar
• Pönisch , G. and Schwetlick , H. 1981 . Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter . Computing , 26 : 107 – 121 .
   Web of Science ®Google Scholar
• Powell , M.J.D. 1979 . “ Algorithms for nonlinear constraints that use Lagrangian functions ” . In Survey on Mathematical Programming Edited by: Prékopa , A. Vol. 1 , 513 – 537 . Budapest
   Google Scholar
• Pšeničnyj , B.N. and Danilin , Ju.M . 1982 . Numerische Methoden für Extremalaufgaben VEB DVW Berlin Übers. a. d. Russ
   Google Scholar
• Sargent , R.W.H. “ Reduced-gradient and projection methods for nonlinear programming ” . In Numerical Methods for Constrained Optimization Edited by: Gill , P.E. and Murray , W.
   Google Scholar
• Schittkowski , K. 1982 . A unified outline of nonlinear programming methods . ASME J. on Mechanics, Transmissions, and Automation in Design ,
   Google Scholar
• Schmidt , J.W. 1981 . On the R-order of coupled sequences . Computing , 26 : 333 – 342 .
   Web of Science ®Google Scholar
• Schmidt , J.W. , Hoyer , W. and Haufe , Ch . 1985 . Consistent approximations in Newton- type decomposition methods . WNumer. Math , 47 : 413 – 425 .
   Web of Science ®Google Scholar
• Schwetlick , H. 1979 . Numerische Losung nichtlinearer Gleichungen VEB DVW Berlin
   Google Scholar
• Schwetlick , H. , Schellong , W. and Teller , V. 1985 . Gauss-Newton-like methods for nonlinear least squares with equality constraints-Local convergence and applications to parameter estimation in implicit models . Statistics , 16 : 167 – 178 .
   Google Scholar
• Smeers , Y. 1977 . Generalized reduced gradient method as an extension of feasible direction methods . JOTA , 22 : 209 – 226 .
   Web of Science ®Google Scholar
• Tapia , R.A. 1974 . A stable approach to Newton's method for general mathematical programming problems in Rn . JOTA , 14 : 453 – 476 .
   Web of Science ®Google Scholar
• Tapia , R.A. 1977 . Diagonalized multiplier methods and quasi-NEWTON methods for constrained optimization . JOTA , 22 : 135 – 194 .
   Web of Science ®Google Scholar