An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

Trust region method is a robust method for optimization problems. In this paper, we propose a novel adaptive nonmonotone technique based on trust region methods for solving unconstrained optimization. In order to accelerate the convergence of trust region methods, an adaptive trust region is generated according to the Hessian of the iterate point. Both the nonmonotone techniques and this adaptive strategies can improve the trust region methods in the sense of convergence. We prove that the proposed method is locally superlinear convergence under some standard assumptions. Numerical results show that the new method is effective and has a high speed of convergence in practice.

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

[2]  Jorge J. Moré,et al.  Benchmarking optimization software with performance profiles , 2001, Math. Program..

[3]  Nicholas I. M. Gould,et al.  CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization , 2013, Computational Optimization and Applications.

[4]  Boying Wu,et al.  A new modified nonmonotone adaptive trust region method for unconstrained optimization , 2012, Comput. Optim. Appl..

[5]  Shengquan Wang,et al.  Nonmonotone adaptive trust region method , 2011, Eur. J. Oper. Res..

[6]  H. Mesgarani,et al.  A new nonmonotone trust region method for unconstrained optimization equipped by an efficient adaptive radius , 2014, Optim. Methods Softw..

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

[8]  Philippe L. Toint,et al.  Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints , 1997, Math. Program..

[9]  R. Varga.  Geršgorin And His Circles , 2004 .

[10]  Charles Audet,et al.  Linear equalities in blackbox optimization , 2014, Comput. Optim. Appl..

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

[12]  Ya-Xiang Yuan,et al.  Optimization Theory and Methods: Nonlinear Programming , 2010 .

[13]  M. Reza Peyghami,et al.  A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems , 2015, Comput. Optim. Appl..

[14]  Masoud Ahookhosh,et al.  Two globally convergent nonmonotone trust-region methods for unconstrained optimization , 2015, 1501.02011.

[15]  Mert Gürbüzbalaban,et al.  On Nesterov's Nonsmooth Chebyshev-Rosenbrock Functions , 2012 .

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

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

[18]  Wu Qing-jun.  Nonmonotone trust region algorithm for unconstrained optimization problems , 2010 .

[19]  Zhenjun Shi,et al.  A new trust region method for unconstrained optimization , 2008 .

[20]  Yigui Ou,et al.  A hybrid trust region algorithm for unconstrained optimization , 2011 .

[21]  Li-Zhi Liao,et al.  An adaptive trust region method and its convergence , 2002 .

[22]  Neculai Andrei,et al.  An Unconstrained Optimization Test Functions Collection , 2008 .