A new accelerated diagonal quasi-Newton updating method with scaled forward finite differences directional derivative for unconstrained optimization. (1st February 2021)

• Record Type: Journal Article
• Authors: Andrei, Neculai
• Is Part Of: Optimization. Volume 70:Number 2(2021)
• Page Start: 345
• Page End: 360
• Publication Date: 2021-02-01
• Subjects: Unconstrained optimization -- diagonal quasi-Newton updating -- Global convergence -- directional derivatives -- numerical comparisons; 49M7 -- 49M10 -- 65K05 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1712391
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : An accelerated diagonal quasi-Newton updating algorithm for unconstrained optimization is presented. The elements of the diagonal matrix approximating the Hessian are determined as scaling of the 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 75 unconstrained optimization test problems, of different structures and complexities, prove that the suggested algorithm is more efficient and more robust than self-scaling memoryless BFGS method of Perry–Shanno with Oren–Spedicato or with Oren–Luenberger scaling parameter. At the same time, our accelerated algorithm is more efficient and more robust than the accelerated diagonal approximation of the Hessian by finite differences. Numerical experiments with five applications from MINPACK-2 collection show that the proposed algorithm is more efficient than the diagonal approximation of the Hessian by the least-change secant updating strategy and minimizing the trace of the matrix.