The Improved Sacant Algorithm Research For Solving Trust Region Subproblem

Trust-region method has always been a kind of computing method which has attracted much attention in the problem of nonlinear optimization.For solving trust region subproblems with the initially proposed quadratic model,the dogleg method is more efficient and faster.Based on the study about double-secant method which is put forward by Wang Xi-yun and Shaoan,this paper mainly aims at the fold-line algorithm and constructs an improved secant algorithm.Part one,based on the existing double-secant method,we draw into the ?rp to get the improved fold-line algorithm which is also named the improved secant algorithm.In the positive definite of Hessian matrix,the astringency of the algorithm is analyzed,and numerical experiments are done.Part two,we use B-P to decompose and amend the improved secant algorithm,so that the algorithm can be converged when the Hessian matrix is the negative definite,and the numerical experiment is done.Part three,we apply the new quasi Newton equation to propose an improved secant algorithm based on MBFGS.By the numerical experiments,it shows that the algorithm can get the better optimum value and fewer iterations.Part four,according to the construction idea of the improved secant method,we can continue dividing and constructing the N-secant algorithm that we can always find the ?_ri+1p in the optimal curve and make the tangent direction of the point be parallel to ?-?_rip.In addition,the convergence of the algorithm is analyzed.