@article{MAKHILLJEAS2018132217168,
    title = {A Modified Trust-Region Method for Solving Unconstrained Optimization},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {13},
    number = {22},
    pages = {9667-9671},
    year = {2018},
    issn = {1816-949x},
    doi = {jeasci.2018.9667.9671},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2018.9667.9671},
    author = {Mushtaq and},
    keywords = {Unconstrained optimization,trust-region method,global convergence,promising,numerical,optimization},
    abstract = {In this research, we present a new radius for a modified trust region method and used them to solve
the large-scale unconstrained optimization. Our approach increases and improves the robustness and efficiency
of the trust-region frameworks as well as decrease the computational cost of the algorithm by decreasing the
number of the trust-region subproblems that must resolved when the trail step rejected. Theoretical analysis
shows that the new approach conserve the global convergence to the first-order critical points under classical
assumptions. Moreover, the superlinear and the quadratic convergence are established under suitable
conditions. The numerical results show that the new method is effective and promising for solving
unconstrained optimization problems.}
    }