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A quasi-Newton method with sparse triple factorization for unconstrained minimization
Authors:Dao-qi Chen  R. P. Tewarson
Affiliation:1. Applied Mathematics and Statistics Department, SUNY at Stony Brook, 11794, New York, NY, U.S.A.
Abstract:A new quasi-Newton method for unconstrained minimization is presented. It uses sparse triple factorization of an approximation to the sparse Hessian matrix. At each step a new column and a corresponding row of the approximation to the Hessian is determined and its triple factorization is updated. Our method deals with the same updating problem as in J. Bräuninger's paper [2]. However, we make use of a rank-two instead of a rank-one updating scheme. Our method saves over half the number of operations required in J. Bräuninger's method. Moreover, our method utilizes the sparsity and, therefore, only the nonzero entries of the factors need to be stored. The positive definiteness can be preserved easily by taking suitable precautions. Under reasonable conditions our method is globally convergent and locally superlinearly evenn-step ρ-order convergent.
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