We propose a new family of trust region algorithms for unconstrained optimization problems which is combining traditional trust region method with a nonmonotone Wolfe line search technique. The new algorithm solves the trust region subproblem only once at each iteration, furthermore, the matrix approximation to the Hessian simultaneously satisfies the quasi-Newton condition at each iteration and maintains its positive definiteness. Under certain conditions, the global convergence and strong global convergence of the algorithm are proved. Numerical results show that the algorithm inherits the advantages of the nonmonotone schemes and is meaningful to some optimization problems.
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