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.
Wen-yu SUN~(1+) Qun-yan ZHOU~(1,2) ~1 School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China
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.
In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.
