On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
TNPACK—A truncated Newton minimization package for large-scale problems: I. Algorithm and usage
ACM Transactions on Mathematical Software (TOMS)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Efficient Implementation of the Truncated-Newton Algorithm for Large-Scale Chemistry Applications
SIAM Journal on Optimization
Molecular Modeling and Simulation: An Interdisciplinary Guide
Molecular Modeling and Simulation: An Interdisciplinary Guide
Computational Optimization and Applications
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To efficiently solve a large scale unconstrained minimization problem with a dense Hessian matrix, this paper proposes to use an incomplete Hessian matrix to define a new modified Newton method, called the incomplete Hessian Newton method (IHN). A theoretical analysis shows that IHN is convergent globally, and has a linear rate of convergence with a properly selected symmetric, positive definite incomplete Hessian matrix. It also shows that the Wolfe conditions hold in IHN with a line search step length of one. As an important application, an effective IHN and a modified IHN, called the truncated-IHN method (T-IHN), are constructed for solving a large scale chemical database optimal projection mapping problem. T-IHN is shown to work well even with indefinite incomplete Hessian matrices. Numerical results confirm the theoretical results of IHN, and demonstrate the promising potential of T-IHN as an efficient minimization algorithm.