Nested Performance Profiles for Benchmarking Software
Abstract
In order to compare and benchmark the mathematical software, the performance profiles have been introduced [1]. However, it has been proved that the algorithm is not flawless. The main issue with the performance profile is that it may rank the solvers with respect to the best solver, by excluding the best one and running the algorithm on the remaining set of the solvers, the method may rank the solvers in a different way. We characterize such systems of problems-solvers and propose an efficient and reliable algorithm to overcome this negative side effect. The proposed method is unbiased in comparing the solvers and is successful in detecting the top ones.References
Dolan, Elizabeth D., and Jorge J. Mor. ”Benchmarking optimization software with performance profiles.” Mathematical programming 91, no. 2 (2002): 201-213.
Benson, Hande Y., David F. Shanno, and Robert J. Vanderbei. ”Interior-point methods for nonconvex nonlinear programming: Jamming and comparative numerical testing.” Operations Research and Financial Engineering, Princeton University, ORFE-00-02 (2000).
Bongartz, I., Conn, A.R., Gould, N.I.M., Saunders, M.A., Toint, P.L. : A numerical comparison between the LANCELOT and MINOS packages for large-scale numerical optimization. Report 97/13, Namur University, (1997)
Conn, Andrew R., Nick Gould, and Ph L. Toint. ”Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization.” Mathematical Programming 73, no. 1 (1996): 73.
Nash, Stephen G., and Jorge Nocedal. ”A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization.” SIAM Journal on Optimization 1, no. 3 (1991): 358-372.
Billups, Stephen C., Steven P. Dirkse, and Michael C. Ferris. ”A comparison of large scale mixed complementarity problem solvers.” Computational Optimization and Applications 7, no. 1 (1997): 3-25.
Gould, Nicholas, and Jennifer Scott. ”A note on performance profiles for benchmarking software.” ACM Transactions on Mathematical Software (TOMS) 43, no. 2 (2016).
See http://www.math.uh.edu/˜rhekmati or https://rasoulhekmati.yolasite.com
See http://www.mcs.anl.gov/˜more/cops
Gould, Nicholas, and Jennifer Scott. ”The state-of-the-art of preconditioners for sparse linear least-squares problems.” ACM Transactions on Mathematical Software (TOMS) 43, no. 4 (2017): 36.
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