title: An incomplete Hessian Newton minimization method and its application in a chemical database problem.
abstract: 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.
authors.affiliation: Department of Mathematical Sciences, University of Wisconsin, 3200 N Cramer Street, EMS Building, Room E403, Milwaukee, WI 53211, USA.
authors.forename: Dexuan
authors.initials: D
authors.lastname: Xie
authors.forename: Qin
authors.initials: Q
authors.lastname: Ni
references.citation: J Chem Inf Comput Sci. 2000 Jan-Feb;40(1):167-77
references.pmid: 10661564