A nonmonotone trust-region method of conic model for unconstrained optimization

In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217-231] with a nonmonotone technique for solving unconstrained optimization. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the method of [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217-231].

[1]  W. Davidon.  Conic Approximations and Collinear Scalings for Optimizers , 1980 .

[2]  Richard H. Byrd,et al.  A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties. , 1985 .

[3]  Ya-Xiang Yuan,et al.  Optimization theory and methods , 2006 .

[4]  Xiang-Sun Zhang,et al.  A nonmonotone adaptive trust region method and its convergence , 2003 .

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

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

[7]  Jorge Nocedal,et al.  Combining Trust Region and Line Search Techniques , 1998 .

[8]  Jiye Han,et al.  A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints , 2001 .

[9]  D. Sorensen.  THE Q-SUPERLINEAR CONVERGENCE OF A COLLINEAR SCALING ALGORITHM FOR UNCONSTRAINED OPTIMIZATION* , 1980 .

[10]  K. A. Ariyawansa.  Deriving collinear scaling algorithms as extensions of quasi-Newton methods and the local convergence of DFP- and BFGS-related collinear scaling algorithms , 1990, Math. Program..

[11]  M. J. D. Powell,et al.  On the global convergence of trust region algorithms for unconstrained minimization , 1984, Math. Program..

[12]  Shao-Jian Qu,et al.  A conic trust-region method for optimization with nonlinear equality and inequality constrains via active-set strategy , 2006, Appl. Math. Comput..

[13]  T. M. Williams,et al.  Practical Methods of Optimization. Vol. 1: Unconstrained Optimization , 1980 .

[14]  Zengxin Wei,et al.  A nonmonotone trust region method for unconstrained optimization , 2005, Appl. Math. Comput..

[15]  Wenyu Sun,et al.  A trust region method for conic model to solve unconstraind optimizaions , 1996 .