Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Inexact trust region method for large sparse systems of nonlinear equations
Journal of Optimization Theory and Applications
Efficient line search algorithm for unconstrained optimization
Journal of Optimization Theory and Applications
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
A new trust region method with adaptive radius
Computational Optimization and Applications
Solving a system of nonlinear integral equations by an RBF network
Computers & Mathematics with Applications
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A new globalization strategy for solving an unconstrained minimization problem is proposed based on the idea of combining Newton's direction and the steepest descent direction WITHIN each iteration. Global convergence is guaranteed with an arbitrary initial point. The search direction in each iteration is chosen to be as close to the Newton's direction as possible and could be the Newton's direction itself. Asymptotically the Newton step will be taken in each iteration and thus the local convergence is quadratic. Numerical experiments are also reported. Possible combination of a Quasi-Newton direction with the steepest descent direction is also considered in our numerical experiments. The differences between the proposed strategy and a few other strategies are also discussed.