In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the ...In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.展开更多
This paper presents a new trust region dogleg method for unconstrained optimization. The method can deal with the case when the Hessian B of quadratic models is indefinite. It is proved that the method is globally...This paper presents a new trust region dogleg method for unconstrained optimization. The method can deal with the case when the Hessian B of quadratic models is indefinite. It is proved that the method is globally convergent and has a quadratic convergence rate if B\+\{(k)\} = Δ\+2 f(x\+\{(k)\}). Under certain conditions, the solution obtained by the method is even a second order stationary point. Numerical results also declare effectiveness of the method.展开更多
基金Supported by the NNSF(10231060 and 10501024)of Chinathe Specialized Research Fund(20040319003)of Doctoral Program of Higher Education of China+1 种基金the Natural Science Grant(BK2006214)of Jiangsu Province of Chinathe Foundation(2004NXY20)of Nanjing Xiaozhuang College.
文摘In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.
文摘This paper presents a new trust region dogleg method for unconstrained optimization. The method can deal with the case when the Hessian B of quadratic models is indefinite. It is proved that the method is globally convergent and has a quadratic convergence rate if B\+\{(k)\} = Δ\+2 f(x\+\{(k)\}). Under certain conditions, the solution obtained by the method is even a second order stationary point. Numerical results also declare effectiveness of the method.
