Convergence analysis of truncated incomplete Hessian Newton minimization method and application in biomolecular potential energy minimization

This paper gives a general convergence analysis to the truncated incomplete Hessian Newton method (T‐IHN). It shows that T‐IHN is globally convergent even with an indefinite incomplete Hessian matrix or an indefinite preconditioner, which may happen in practice. It also proves that when the T‐IHN iterates are close enough to a minimum point, T‐IHN has a Q‐linear rate of convergence, and an admissible line search steplength of one. Moreover, a particular T‐IHN algorithm is constructed for minimizing a biomolecular potential energy function, and numerically tested for a protein model problem based on a widely used molecular simulation package, CHARMM. Numerical results confirm the theoretical results, and demonstrate that T‐IHN can have a better performance (in terms of computer CPU time) than most CHARMM minimizers.