The {ao}
package implements a numerical optimization algorithm called alternating optimization in R.
Alternating optimization is an iterative procedure which optimizes a function jointly over all parameters by alternately performing restricted optimization over individual parameter subsets.
For additional details on the method, please refer to the package vignette.
You can install the released version of {ao}
from CRAN with:
The following is a simple example to perform alternating optimization of the Himmelblau’s function, separately for \(x_1\) and \(x_2\), with the parameter restrictions \(-5 \leq x_1, x_2 \leq 5\).
library("ao")
#> Loading required package: optimizeR
#> Thanks for using {ao} version 0.3.3, happy alternating optimization!
#> Documentation: https://loelschlaeger.de/ao
The function is optimized over its first argument (x
), which needs to be a numeric
vector
. Other function arguments (a
and b
in this case) remain fixed during the optimization. The function should return a single numeric
value.
Alternating optimization requires a base optimizer that numerically solves the optimization problems in the partitions of the parameter vector. Such an optimizer must be defined through the framework provided by the {optimizeR}
package, please see its documentation for details.
ao()
functionDespite f
and base_optimizer
, which have been defined above, the ao()
function requires the following arguments:
p
defines the starting parameter values,
a
and b
are fixed function arguments,
partition
defines the parameter subsets (here, the first entry of x
and the second are optimized separately).
ao(f = himmelblau, p = c(0, 0), a = -11, b = -7, partition = list(1, 2), base_optimizer = base_optimizer)
#> $value
#> [1] 1.940035e-12
#>
#> $estimate
#> [1] 3.584428 -1.848126
#>
#> $sequence
#> iteration partition value seconds p1 p2
#> 1 0 NA 1.700000e+02 0.0000000000 0.000000 0.000000
#> 2 1 1 1.327270e+01 0.0090060234 3.395691 0.000000
#> 3 1 2 1.743666e+00 0.0009770393 3.395691 -1.803183
#> 4 2 1 2.847292e-02 0.0007698536 3.581412 -1.803183
#> 5 2 2 4.687472e-04 0.0006618500 3.581412 -1.847412
#> 6 3 1 7.368063e-06 0.0011827946 3.584381 -1.847412
#> 7 3 2 1.157612e-07 0.0004611015 3.584381 -1.848115
#> 8 4 1 1.900153e-09 0.0004670620 3.584427 -1.848115
#> 9 4 2 4.221429e-11 0.0003750324 3.584427 -1.848126
#> 10 5 1 3.598278e-12 0.0004618168 3.584428 -1.848126
#> 11 5 2 1.940035e-12 0.0003538132 3.584428 -1.848126
#>
#> $seconds
#> [1] 0.01471639
The output contains:
the function value
at convergence,
the parameter value estimate
at convergence,
sequence
provides information about the updates in the single iterations and partitions,
and the optimization time in seconds
.
Have a question, found a bug, request a feature, want to contribute? Please file an issue.