I seem to recall hearing the story that the Barzilai-Borwein method (a first-order optimization method with superlinear convergence) was discovered by accident, involving some indexing error in some numerical code. I cannot find any reference. Can anyone confirm or contradict this statement with some reference? Thanks a bunch!
2026-03-28 10:04:27.1774692267
History of the Barzilai-Borwein method
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An interesting myth. I designed the algorithm in 1982 following my Ph.D. work on 2-point algorithms (see J. Barzilai and A. Ben-Tal, “Nonpolynomial and Inverse Interpolation for Line Search: Synthesis and Convergence Rates,” SIAM J. Numer. Anal., Vol. 19, pp. 1263—1277, 1982). The point of this algorithm is to show that the behavior of the steepest descent algorithm cannot be attributed to its search direction.
Jonathan Barzilai