A modified Technique for Solving
Unconstrained Optimization
Mushtaq A.K. Shiker Zahra Sahib
Department of Mathematics,
Collage of Education for Pure Science,
University of Babylon.
mmttmmhh@yahoo.com hussainaldeen@yahoo.com
Abstract. In this work, 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.

Keywords: Unconstrained optimization, Trust-region method, global convergence.