On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
TNPACK—A truncated Newton minimization package for large-scale problems: I. Algorithm and usage
ACM Transactions on Mathematical Software (TOMS)
Hybrid methods for large sparse nonlinear least squares
Journal of Optimization Theory and Applications
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
ACM Transactions on Mathematical Software (TOMS)
Variable metric methods for unconstrainted optimization and nonlinear least squares
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
An Unconstrained Optimization Algorithm Which Uses Function and Gradient Values
An Unconstrained Optimization Algorithm Which Uses Function and Gradient Values
Shifted limited-memory variable metric methods for large-scale unconstrained optimization
Journal of Computational and Applied Mathematics
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We present 14 basic Fortran subroutines for large-scale unconstrained and box constrained optimization and large-scale systems of nonlinear equations. Subroutines PLIS and PLIP, intended for dense general optimization problems, are based on limited-memory variable metric methods. Subroutine PNET, also intended for dense general optimization problems, is based on an inexact truncated Newton method. Subroutines PNED and PNEC, intended for sparse general optimization problems, are based on modifications of the discrete Newton method. Subroutines PSED and PSEC, intended for partially separable optimization problems, are based on partitioned variable metric updates. Subroutine PSEN, intended for nonsmooth partially separable optimization problems, is based on partitioned variable metric updates and on an aggregation of subgradients. Subroutines PGAD and PGAC, intended for sparse nonlinear least-squares problems, are based on modifications and corrections of the Gauss-Newton method. Subroutine PMAX, intended for minimization of a maximum value (minimax), is based on the primal line-search interior-point method. Subroutine PSUM, intended for minimization of a sum of absolute values, is based on the primal trust-region interior-point method. Subroutines PEQN and PEQL, intended for sparse systems of nonlinear equations, are based on the discrete Newton method and the inverse column-update quasi-Newton method, respectively. Besides the description of methods and codes, we propose computational experiments which demonstrate the efficiency of the proposed algorithms.