ucminf
General-Purpose Unconstrained Non-Linear Optimization
An algorithm for general-purpose unconstrained non-linear optimization. The algorithm is of quasi-Newton type with BFGS updating of the inverse Hessian and soft line search with a trust region type monitoring of the input to the line search algorithm. The interface of 'ucminf' is designed for easy interchange with 'optim'.
ucminf
The goal of ucminf is to provide an algorithm for general-purpose
unconstrained non-linear optimization. The algorithm is of quasi-Newton
type with BFGS updating of the inverse Hessian and soft line search with
a trust region type monitoring of the input to the line search
algorithm. The interface of ucminf is designed for easy interchange
with optim
Installation
You can install the development version of ucminf from GitHub with:
# install.packages("devtools")
devtools::install_github("hdakpo/ucminf")
Example
library(ucminf)
# Rosenbrock Banana function
fR <- function(x) (1 - x[1])^2 + 100 * (x[2] - x[1]^2)^2
gR <- function(x) c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
200 * (x[2] - x[1] * x[1]))
## Find minimum and show trace
optRes <- ucminf(par = c(2,.5), fn = fR, gr = gR, control = list(trace = 1))
#> neval = 1, F(x) = 1.2260e+03, max|g(x)| = 2.8020e+03
#> x = 2.0000e+00, 5.0000e-01
#> Line search: alpha = 1.0000e+00, dphi(0) =-2.8881e+03, dphi(1) =-1.4263e+02
#> neval = 2, F(x) = 1.0123e+01, max|g(x)| = 1.3111e+02
#> x = 1.0298e+00, 7.4237e-01
#> Line search: alpha = 1.0000e+00, dphi(0) =-3.1743e+01, dphi(1) = 1.0180e+01
#> neval = 3, F(x) = 1.7049e+00, max|g(x)| = 6.3969e+01
#> x = 1.2600e+00, 1.7155e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-2.5788e+00, dphi(1) =-5.6182e-01
#> neval = 4, F(x) = 1.1612e-01, max|g(x)| = 1.2343e+01
#> x = 1.2174e+00, 1.5083e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-1.5867e-01, dphi(1) = 1.2108e-02
#> neval = 5, F(x) = 4.2253e-02, max|g(x)| = 1.8638e+00
#> x = 1.2033e+00, 1.4449e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-1.1826e-03, dphi(1) =-3.2371e-04
#> neval = 6, F(x) = 4.1500e-02, max|g(x)| = 8.6681e-01
#> x = 1.2035e+00, 1.4474e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-5.9673e-04, dphi(1) =-4.7194e-04
#> neval = 7, F(x) = 4.0965e-02, max|g(x)| = 4.8839e-01
#> x = 1.2024e+00, 1.4456e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-3.9731e-03, dphi(1) =-2.3018e-03
#> neval = 8, F(x) = 3.7853e-02, max|g(x)| = 8.5215e-01
#> x = 1.1928e+00, 1.4254e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-8.0453e-03, dphi(1) =-6.3954e-03
#> neval = 9, F(x) = 3.0800e-02, max|g(x)| = 2.0990e+00
#> x = 1.1676e+00, 1.3685e+00
#> Line search: alpha = 8.2084e-01, dphi(0) =-4.4175e-02, dphi(1) = 1.8746e-02
#> neval = 11, F(x) = 4.8486e-03, max|g(x)| = 2.2862e+00
#> x = 1.0458e+00, 1.0884e+00
#> Line search: alpha = 3.8293e-01, dphi(0) =-4.8734e-03, dphi(1) = 4.6817e-04
#> neval = 13, F(x) = 4.0485e-03, max|g(x)| = 1.1863e+00
#> x = 1.0584e+00, 1.1177e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-6.4354e-04, dphi(1) =-5.6879e-04
#> neval = 14, F(x) = 3.4426e-03, max|g(x)| = 1.1238e+00
#> x = 1.0535e+00, 1.1074e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-4.7371e-03, dphi(1) =-1.0920e-03
#> neval = 15, F(x) = 6.1678e-04, max|g(x)| = 7.3075e-01
#> x = 1.0180e+00, 1.0347e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-7.9043e-04, dphi(1) =-2.5377e-04
#> neval = 16, F(x) = 1.0437e-04, max|g(x)| = 1.6394e-01
#> x = 1.0096e+00, 1.0189e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-1.8089e-04, dphi(1) =-1.8237e-05
#> neval = 17, F(x) = 5.8219e-06, max|g(x)| = 9.1455e-02
#> x = 1.0009e+00, 1.0016e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-1.3102e-05, dphi(1) = 2.0222e-06
#> neval = 18, F(x) = 2.9162e-07, max|g(x)| = 1.7185e-02
#> x = 1.0003e+00, 1.0007e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-5.9332e-07, dphi(1) = 1.1234e-08
#> neval = 19, F(x) = 1.2578e-10, max|g(x)| = 2.0751e-04
#> x = 9.9999e-01, 9.9998e-01
#> Line search: alpha = 1.0000e+00, dphi(0) =-2.5270e-10, dphi(1) = 1.1297e-12
#> neval = 20, F(x) = 3.5670e-15, max|g(x)| = 2.0836e-06
#> x = 1.0000e+00, 1.0000e+00
#> Line search: alpha = 1.0000e+00, dphi(0) =-7.1150e-15, dphi(1) =-1.8980e-17
#> Optimization has converged
#> Stopped by small gradient (grtol).
#> maxgradient laststep stepmax neval
#> 1.020598e-08 6.480989e-08 1.225000e-01 2.100000e+01