A New Diagonal Quasi-Newton Updating Method With Scaled Forward Finite Differences Directional Derivative for Unconstrained Optimization. (3rd October 2019)

• Record Type: Journal Article
• Authors: Andrei, Neculai
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 13(2019)
• Page Start: 1467
• Page End: 1488
• Publication Date: 2019-10-03
• Subjects: Diagonal quasi-Newton updating -- directional derivatives;global convergence -- numerical comparisons -- unconstrained optimization; 49M7 -- 49M10 -- 65K05 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1552293
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: A new diagonal quasi-Newton updating algorithm for unconstrained optimization is presented. The elements of the diagonal matrix approximating the Hessian are determined as scaled forward finite differences directional derivatives of the components of the gradient. Under mild classical assumptions, the convergence of the algorithm is proved to be linear. Numerical experiments with 80 unconstrained optimization test problems, of different structures and complexities, as well as five applications from MINPACK-2 collection, prove that the suggested algorithm is more efficient and more robust than the quasi-Newton diagonal algorithm retaining only the diagonal elements of the BFGS update, than the weak quasi-Newton diagonal algorithm, than the quasi-Cauchy diagonal algorithm, than the diagonal approximation of the Hessian by the least-change secant updating strategy and minimizing the trace of the matrix, than the Cauchy with Oren and Luenberger scaling algorithm in its complementary form (i.e. the Barzilai-Borwein algorithm), than the steepest descent algorithm, and than the classical BFGS algorithm. However, our algorithm is inferior to the limited memory BFGS algorithm (L-BFGS).