Solver for unconstrainted minimization problems
math/liblbfgs (package's history)
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liblbfgs 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: 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. Among the various ports of L-BFGS, this library provides several features: * Optimization with L1-norm (Orthant-Wise Limited-memory Quasi-Newton (OWL-QN) method): In addition to standard minimization problems, the library can minimize a function F(x) combined with L1-norm |x| of the variables, {F(x) + C |x|}, where C is a constant scalar parameter. This feature is useful for estimating parameters of sparse log-linear models (e.g., logistic regression and maximum entropy) with L1-regularization (or Laplacian prior). * Clean C code: Unlike C codes generated automatically by f2c (Fortran 77 into C converter), this port includes changes based on my interpretations, improvements, optimizations, and clean-ups so that the ported code would be well-suited for a C code. In addition to comments inherited from the original code, a number of comments were added through my interpretations. * Callback interface: The library receives function and gradient values via a callback interface. The library also notifies the progress of the optimization by invoking a callback function. In the original implementation, a user had to set function and gradient values every time the function returns for obtaining updated values. * Thread safe: The library is thread-safe, which is the secondary gain from the callback interface. * Cross platform. The source code can be compiled on Microsoft Visual Studio 2005, GNU C Compiler (gcc), etc. * Configurable precision: A user can choose single-precision (float) or double-precision (double) accuracy by changing LBFGS_FLOAT macro. * SSE/SSE2 optimization: This library includes SSE/SSE2 optimization (written in compiler intrinsics) for vector arithmetic operations on Intel/AMD processors. The library uses SSE for float values and SSE2 for double values. The SSE/SSE2 optimization routine is disabled by default.
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