An unconstrained optimization method using nonmonotone second order Goldstein’s line search

In this paper, an unconstrained optimization method using the nonmonotone second order Goldstein’s line search is proposed. By using the negative curvature information from the Hessian, the sequence generated is shown to converge to a stationary point with the second order optimality conditions. Numerical tests on a set of standard test problems confirm the efficiency of our new method.

[1]  L. Grippo,et al.  A nonmonotone line search technique for Newton's method , 1986 .

[2]  F. Lampariello,et al.  Use of the Minimum-Norm Search Direction in a Nonmonotone Version of the Gauss-Newton Method , 2003 .

[3]  N. Deng,et al.  Nonmonotonic trust region algorithm , 1993 .

[4]  Danny C. Sorensen,et al.  On the use of directions of negative curvature in a modified newton method , 1979, Math. Program..

[5]  Jorge J. Moré,et al.  Testing Unconstrained Optimization Software , 1981, TOMS.

[6]  Michael C. Ferris,et al.  Nonmonotone curvilinear line search methods for unconstrained optimization , 1996, Comput. Optim. Appl..

[7]  Garth P. McCormick,et al.  A modification of Armijo's step-size rule for negative curvature , 1977, Math. Program..

[8]  Stefano Lucidi,et al.  Curvilinear Stabilization Techniques for Truncated Newton Methods in Large Scale Unconstrained Optimization , 1998, SIAM J. Optim..

[9]  J. Bunch,et al.  Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations , 1971 .

[10]  Chengxian Xu,et al.  A Class of Indefinite Dogleg Path Methods for Unconstrained Minimization , 1999, SIAM J. Optim..

[11]  Wenyu Sun,et al.  Nonmonotone trust region method for solving optimization problems , 2004, Appl. Math. Comput..

[12]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[13]  Wenyu Sun,et al.  Global convergence of nonmonotone descent methods for unconstrained optimization problems , 2002 .

[14]  Wenyu Sun,et al.  Nonmonotone adaptive trust-region method for unconstrained optimization problems , 2005, Appl. Math. Comput..

[15]  Donald Goldfarb,et al.  Curvilinear path steplength algorithms for minimization which use directions of negative curvature , 1980, Math. Program..