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This function calculates the quasi-Newton update with the gradient history, giving the search direction. Based on the BFGS algorithm, this limited-memory BFGS (L-BFGS) algorithm stores only few vectors that implicitly represent the approximation of the BFGS algorithm (which stores a matrix equal to the number of optimisation variables)




This function is the implementation from section 4 of


    x_hist         - vector array of waveform history, num_var x size_store

    df_hist        - vector array of gradient history, num_var x size_store

    grad           - vector of the current gradient, (num_vars x 1)

    N              - number of waveform/gradient vectors to store (default=20)


    direction      - the vector giving the BFGS approximation to the search direction


The L-BFGS algorithm is the default of fminnewton.m, and should be considered a good mix of computational efficiency and fast convergence.

See also

quasinewton.m, fminnewton.m, optim_tols.m

Version 1.9, authors: Ilya Kuprov, David Goodwin