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.
Highlights
Researchers working in different areas, for instance, in economics, engineering, data mining and machine learning encounter different types of optimization problems including those with smooth, non-smooth, convex or nonconvex objective and/or constraint functions
Since it is not possible to give all of the 20 results obtained for each of the 36 test problems mentioned in the previous section, we first give the table below, which presents HANSO and BFGS solves how many problems related to the starting points successfully
On the other hand, looking at the values of the problems CB3, DEM, Polak 3, Wong 3, WF, SPIRAL, El-Attar, and Gill from Tables 3 and 4., one can observe that both HANSO and BFGS were able to solve them for some starting points
Summary
Researchers working in different areas, for instance, in economics, engineering, data mining and machine learning encounter different types of optimization problems including those with smooth, non-smooth, convex or nonconvex objective and/or constraint functions. While these researchers search for an optimal solution of their real-life problems, they need suitable software. The theory and application of engineering problems can be found in [4], in particular, some genetic engineering problems are discussed in [5, 6] In the areas such as data mining, machine learning and control theory the sources [7,8,9] are very useful and important for readers. It is possible to increase the examples in the application area, but it is useful to talk about HANSO software as soon as possible without going beyond our purpose
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