An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems

Based on a modified secant equation, we propose a scalar approximation of the Hessian to be used in the trust region subproblem. Then, we suggest an adaptive nonmonotone trust region algorithm with a simple quadratic model. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan-Moré performance profile. They demonstrate efficiency of the proposed algorithm.