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We propose a new class of trust region method with a self-adaptive trust region radius update rules. Trust region radius is automatically adjusted according to the weighted sum of the ratios between the actual reduction and the prediction reduction. At some assumptions, the global convergence are proved. Finally, numerical experiments show that the method is robust and effective.
We propose a trust region modified BFGS method that employs the filter technique. At some assumptions, the global convergence is proposed to a first-order stationary point and a second-order stationary point.
We propose a new trust region method that employs both the modified BFGS update and Amijio line search. The method exploits the information of function and gradient, and ensures the Hessian matrix of trust region subproblem positive-definite. At some assumptions, the global convergence and superlinear convergence property are proposed. Finally, numerical experiments show that the method is efficient.
We propose a new switching method for unconstrained minimization. The method is based on the quasi-Newton updates of Hiroshi Yabe, Hideho Ogasawara and Masayuki Yoshino. The eigenvalues and condition numbers of the modified SR1 update and the modified BFGS update are evaluated and used in the switching rule. When the condition number of the former is superior to that of the latter, the step is the...
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