Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method

• Main Authors: Leong, Wah June, Farid, Mahboubeh, Abu Hassan, Malik
• Format: Article
• Language: English
• Published: ICI Publishing House 2010
• Online Access: http://psasir.upm.edu.my/id/eprint/17711/1/Improved_Hessian_Approximation_with_Modified_Quasi-_Cauchy_Relation_for_a_Gradient-type_Method.pdf; http://psasir.upm.edu.my/id/eprint/17711/; https://camo.ici.ro/journal/v12n1.htm

In this work we develop a new gradient-type method with improved Hessian approximation for unconstrained optimization problems. The new method resembles the Barzilai-Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of the identity matrix in the BB method. Then the diagonal Hessian approximation is derived based on the quasi-Cauchy relation. To further improve the Hessian approximation, we modify the quasi-Cauchy relation to carry some additional information from the values and gradients of the objective function. Numerical experiments show that the proposed method yields desirable improvement.