General-Purpose Unconstrained Non-Linear Optimization.

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