Composite Test Functions for Benchmarking Nonlinear Optimization Software

doi:10.3390/math13213524

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Composite Test Functions for Benchmarking Nonlinear Optimization Software

2025-11-03

János D. Pintér *

DOI：10.3390/math13213524

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Abstract

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Nonlinear optimization (NLO) is widely applicable to model and solve decision problems arising in engineering, economic, financial, and scientific studies. Due to the general scope of NLO, optimization model difficulty varies substantially, requiring the utilization of robust, efficient, and flexible solver software. In order to develop constructive guidelines regarding suitable software choices, broad, representative, and reproducible classes of test problems are needed. In this article, we propose flexible and expandable classes of composite test functions, based on earlier introduced or brand-new test problems with known solutions. In our illustrative tests, we use the high-level computing system Mathematica as a model development platform, with some of its readily available NLO solver options. The suggested general approach can be easily adapted to develop benchmarking studies using other modeling environments, test model collections, and solver options.

Keywords:

nonlinear optimization

software testing and benchmarking

composite test functions

Mathematica model development and computing system

illustrative results