A modified Newton direction for unconstrained optimization

References

• Biazar , J and Ghanbari , B . 2009 . A modification on Newton's method for solving systems of non-linear equations . World Acad. Sci. Eng. Tech. , 58 : 897 – 901 .
   Google Scholar
• Dennis , JE Jr . 1968 . On Newton-like methods . Numer. Math. , 11 : 324 – 330 .
   Web of Science ®Google Scholar
• Dennis , JE Jr and More , JJ . 1977 . Quasi-Newton methods, motivation and theory . SIAM Rev. , 19 : 46 – 89 .
   Web of Science ®Google Scholar
• Dennis , JE Jr and Schnabel , RB . 1983 . Numerical Methods for Unconstrained Optimization and Nonlinear Equations , Englewood Cliffs , , NJ : Prentice-Hall, Inc. .
   Google Scholar
• Dieudonne , J . 1969 . Foundations of Modern Analysis , New York : Academic Press .
   Google Scholar
• Fletcher , R . 1980 . Practical Methods of Optimization , Vol. 1 , New York : John Wiley .
   Google Scholar
• Gould , NIM , Sainvitu , C and Toint , PhL . 2005 . A filter-trust-region method for unconstrained optimization . SIAM J. Optim. , 16 : 341 – 357 .
   Web of Science ®Google Scholar
• Gould , NIM and Toint , PhL . 2007 . FILTRANE, a Fortran 95 filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems . ACM Trans. Math. Soft. , 33 : 3 – 25 .
   Web of Science ®Google Scholar
• Grapsa , TN . 2007 . “ Implementing the initialization-dependence and the singularity difficulties in Newton's method 07-03 ” . In Tech. Rep., Department of Mathematics , Patras , , Greece : University of Patras .
   Google Scholar
• Grapsa , TN and Vrahatis , MN . 1990 . A dimension-reducing method for solving systems of non-linear equations in ℛ n . Intern. J. Comput. Math. , 32 : 205 – 216 .
   Web of Science ®Google Scholar
• Grapsa , T and Vrahatis , M . 1996 . A dimension-reducing method for unconstrained optimization . J. Comput. Appl. Math. , 66 : 239 – 253 .
   Web of Science ®Google Scholar
• Grippo , L , Lampariello , F and Lucidi , S . 1986 . A non-monotone line search technique for Newton's method . SIAM J. Numer. Anal. , 23 : 707 – 716 .
   Web of Science ®Google Scholar
• Judd , KL . 1998 . Numerical Methods in Economics , Cambridge : The MIT Press .
   Google Scholar
• Kostopoulos , AE , Androulakis , GS and Grapsa , TN . 2009 . “ A new non-monotone Newton's modification for unconstrained optimization ” . In Tech. Rep. 09-05, Department of Mathematics , Patras , , Greece : University of Patras .
   Google Scholar
• Krejić , N , Luanin , Z and Stojkovska , I . 2009 . Gauss-Newton-based BFGS method with filter for unconstrained minimization . Appl. Math. Comput. , 211 : 354 – 362 .
   Web of Science ®Google Scholar
• Malihoutsaki , EN , Nikas , IA and Grapsa , TN . 2009 . Improved Newton's method without direct function evaluations . J. Comput. Appl. Math. , 227 : 206 – 212 .
   Web of Science ®Google Scholar
• Miao , W and Sun , W . 2007 . A filter trust-region method for unconstrained optimization problems . Numer. Math. J. Chin. Univ. , 29 : 88 – 96 .
   Google Scholar
• Miettinen , K . 1999 . Nonlinear Multiobjective Optimization , Boston : Kluwer Academic Publishers .
   Google Scholar
• Nocedal , J . 1992 . Theory of algorithms for unconstrained optimization . Acta Numerica , 1 : 199 – 242 .
   Google Scholar
• Nocedal , J and Wright , SJ . 1999 . Numerical Optimization , New York : Springer-Vergan .
   Google Scholar
• Ortega , JM . 1972 . Numerical Analysis , New York : Academic Press .
   Google Scholar
• Ortega , M and Rheinboldt , WC . 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
   Google Scholar
• Ostrowski , A . 1973 . Solutions of Equations in Euclidean and Banach Spaces , 3rd , London : Academic Press .
   Google Scholar
• Traub , JF . 1964 . Iterative Methods for the Solution of Equations , Englewood Cliffs , , NJ : Prentice-Hall, Inc. .
   Google Scholar
• Vrahatis , MN . 1988 . CHABIS: A mathematical software package for locating and evaluating roots of systems of non-linear equations . ACM Trans. Math. Soft. , 14 : 330 – 336 .
   Web of Science ®Google Scholar
• Vrahatis , MN and Iordanidis , KI . 1986 . A rapid generalized method of bisection for solving systems of non-linear equations . Numer. Math. , 49 : 123 – 138 .
   Web of Science ®Google Scholar
• Zhang , Y , Sun , W and Qi , L . 2010 . A Nonmonotone filter Barzilai–Borwein method for optimization . Asia-Pacific J. Oper. Res. , 27 : 55 – 69 .
   Web of Science ®Google Scholar