libLBFGS: a library of Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)
This library is a C port of the implementation of Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method written by Jorge Nocedal. The original FORTRAN source code is available at: http://www.ece.northwestern.edu/~nocedal/lbfgs.html
The L-BFGS method solves the unconstrainted minimization problem,
minimize F(x), x = (x1, x2, ..., xN),
only if the objective function F(x) and its gradient G(x) are computable. The well-known Newton's method requires computation of the inverse of the hessian matrix of the objective function. However, the computational cost for the inverse hessian matrix is expensive especially when the objective function takes a large number of variables. The L-BFGS method iteratively finds a minimizer by approximating the inverse hessian matrix by information from last m iterations. This innovation saves the memory storage and computational time drastically for large-scaled problems.