Computing the Sparsity Pattern of Hessians Using Automatic Differentiation

Autor(es)

Gower, Robert Mansel ^[1] ; Mello, Margarida Pinheiro ^[2]

Afiliação do(s) autor(es)

^[1] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH8 9YL, Midlothian - Scotland

^[2] Univ Estadual Campinas, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE; v. 40, n. 2 FEB 2014.
• Citações Web of Science: 3

Resumo

We compare two methods that calculate the sparsity pattern of Hessian matrices using the computational framework of automatic differentiation. The first method is a forward-mode algorithm by Andrea Walther in 2008 which has been implemented as the driver called hess\_pat in the automatic differentiation package ADOL-C. The second is edge\_push\_sp, a new reverse mode algorithm descended from the edge pushing algorithm for calculating Hessians by Gower and Mello in 2012. We present complexity analysis and perform numerical tests for both algorithms. The results show that the new reverse algorithm is very promising. (AU)

• Processo FAPESP: 06/53768-0 - Métodos computacionais de otimização
• Beneficiário: José Mário Martinez Perez
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 09/04785-7 - Differenciação automática de matrizes Hessianas
• Beneficiário: Robert Mansel Gower
• Modalidade de apoio: Bolsas no Brasil - Mestrado