Research Of Trust Region Algorithm And Radius Adjustment Based On New Conic Model

Trust region algorithm has good convergence and stability. For solving nonlinearoptimization problems, especially the unconstrained optimization problem, it is a kindof important numerical calculation method. So it has been widely promoted by theoptimization research, especially in recent ten years, this approach has become a hotspotin the research of the optimization problem. In the traditional trust region mothed, theobjection function can be approximated by using the quadratic model. However, forsome functions which have strongly non-quadratic form and more severe curvaturechange, the trust region algorithm of the conic model has some advantages in practicalcalculation algorithm. The trust region algorithm of new conic model is proposed byNi-Qin, who considered the more general situation of the conic model’s subproblems.The algorithm overcomes that the cone function may unboundedness, which has brokenthrough the limitation of the trust region radius and the horizontal vector.This article mainly studies the algorithm frame’s structure and improvement. It isdivided into four chapters. In the first chapter, the generation and development of thetrust region algorithm based on the new conic model is introduced. In the secondchapter, the traditional trust region algorithm and the trust region algorithm based on theconic model are introduced, and the new conic model trust region algorithm for solvingthe subproblem is analysised. In the third chapter, combining the better convergence oftrust region algorithm and the less computation of line search method, the nonmonotoneWolfe line search technique was applied to the trust region algorithm based on the conicmodel for constructing a trust region algorithm of new conic model with line search.Under proper conditions, the global convergence of the algorithm is proved. Somenumerical results are reported,which confirms the effectiveness of the proposedtechnique. In the forth chapter, Weight and nonmonotone technology is applied to theadaptive trust region method. Under general conditions,the global convergence resultsof the new method are proved. Numerical experiments show that the new method isvery efficient.