Comparative assessment of smooth and non-smooth optimization solvers in HANSO software

Ali Hakan Tor

doi:10.11121/ijocta.2022.1027

Authors

Ali Hakan Tor Abdullah Gül University, Department of Applied Mathematics, Turkey https://orcid.org/0000-0003-3193-5004

DOI:

https://doi.org/10.11121/ijocta.2022.1027

Keywords:

Non-smooth optimization software, BFGS, gradient sampling algorithm, hybrid algorithm

Abstract

The aim of this study is to compare the performance of smooth and nonsmooth optimization solvers from HANSO (Hybrid Algorithm for Nonsmooth Optimization) software. The smooth optimization solver is the implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and the nonsmooth optimization solver is the Hybrid Algorithm for Nonsmooth Optimization. More precisely, the nonsmooth optimization algorithm is the combination of the BFGS and the Gradient Sampling Algorithm (GSA). We use well-known collection of academic test problems for nonsmooth optimization containing both convex and nonconvex problems. The motivation for this research is the importance of the comparative assessment of smooth optimization methods for solving nonsmooth optimization problems. This assessment will demonstrate how successful is the BFGS method for solving nonsmooth optimization problems in comparison with the nonsmooth optimization solver from HANSO. Performance profiles using the number iterations, the number of function evaluations and the number of subgradient evaluations are used to compare solvers.

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Author Biography

Ali Hakan Tor, Abdullah Gül University, Department of Applied Mathematics, Turkey

is an assistant professor at the Department of Mathematics, Abdullah Gul University, Kayseri, Turkey. He received his PhD degree from the Middle East Technical University, Ankara, Turkey in 2013. His research interests include non-smooth optimization theory and numerical non-smooth optimization.

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