The paper "Testing Unconstrained Optimization Software" by Jorge J. Moré, Burton S. Garbow, and Kenneth E. Hillstrom addresses the inadequacies in the testing of optimization software, particularly the small number of test functions and the tendency to use starting points close to the solution. The authors propose a large collection of test functions and guidelines to enhance the reliability and robustness of unconstrained optimization software. They emphasize the importance of testing algorithms on a wide range of functions and starting points to ensure their performance across different scenarios. The paper includes detailed descriptions of the basic subroutines for defining test functions and starting points, as well as specific test functions for nonlinear equations, nonlinear least squares, and unconstrained minimization. The authors also provide examples of how these subroutines can be used to test algorithms and compare their performance. The testing procedures are illustrated through comparisons of two nonlinear least squares subroutines, NLSQ1 and NLSQ2, and two systems of nonlinear equations solvers, NEQ1 and NEQ2, demonstrating the effectiveness of the proposed methods in identifying differences in algorithm performance.The paper "Testing Unconstrained Optimization Software" by Jorge J. Moré, Burton S. Garbow, and Kenneth E. Hillstrom addresses the inadequacies in the testing of optimization software, particularly the small number of test functions and the tendency to use starting points close to the solution. The authors propose a large collection of test functions and guidelines to enhance the reliability and robustness of unconstrained optimization software. They emphasize the importance of testing algorithms on a wide range of functions and starting points to ensure their performance across different scenarios. The paper includes detailed descriptions of the basic subroutines for defining test functions and starting points, as well as specific test functions for nonlinear equations, nonlinear least squares, and unconstrained minimization. The authors also provide examples of how these subroutines can be used to test algorithms and compare their performance. The testing procedures are illustrated through comparisons of two nonlinear least squares subroutines, NLSQ1 and NLSQ2, and two systems of nonlinear equations solvers, NEQ1 and NEQ2, demonstrating the effectiveness of the proposed methods in identifying differences in algorithm performance.