Diagonal Hessian Approximation for Limited Memory Quasi-Newton via Variational Principle | Zendy

S. M. Marjugi | Zendy; Wah June Leong | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Diagonal Hessian Approximation for Limited Memory Quasi-Newton via Variational Principle

Author(s) -

S. M. Marjugi,

Wah June Leong

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/523476

Subject(s) - hessian matrix , diagonal , positive definiteness , mathematics , diagonal matrix , definiteness , quasi newton method , broyden–fletcher–goldfarb–shanno algorithm , main diagonal , inverse , matrix (chemical analysis) , newton's method , mathematical analysis , positive definite matrix , computer science , geometry , physics , nonlinear system , computer network , eigenvalues and eigenvectors , linguistics , philosophy , asynchronous communication , quantum mechanics , materials science , composite material

This paper proposes some diagonal matrices that approximate the (inverse) Hessian by parts using the variational principle that is analogous to the one employed in constructing quasi-Newton updates. The way we derive our approximations is inspired by the least change secant updating approach, in which we let the diagonal approximation be the sum of two diagonal matrices where the first diagonal matrix carries information of the local Hessian, while the second diagonal matrix is chosen so as to induce positive definiteness of the diagonal approximation at a whole. Some numerical results are alsopresented to illustrate the effectiveness of our approximating matrices when incorporated within the L-BFGS algorithm

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research