Help for package ino

Title:

Initialization of Numerical Optimization

Version:

1.1.1

Description:

Analysis of the initialization for numerical optimization of real-valued functions, particularly likelihood functions of statistical models. See https://loelschlaeger.de/ino/ for more details.

License:

GPL (≥ 3)

Encoding:

UTF-8

RoxygenNote:

7.3.2

Depends:

R (≥ 4.1.0)

Imports:

checkmate, cli, dplyr, future.apply, ggplot2, normalize (≥ 0.1.2), oeli (≥ 0.7.4), optimizeR (≥ 1.2.1), portion (≥ 0.1.2), R6, tidyr, utils

Suggests:

knitr, fHMM (≥ 1.4.2), progressr, renv, rmarkdown, scales, TestFunctions, testthat

Config/testthat/edition:

URL:

https://loelschlaeger.de/ino/, https://github.com/loelschlaeger/ino

BugReports:

https://github.com/loelschlaeger/ino/issues

VignetteBuilder:

knitr

LazyData:

true

NeedsCompilation:

Packaged:

2025-10-21 09:22:36 UTC; Lennart Oelschläger

Author:

Lennart Oelschläger

[aut, cre], Marius Ötting

[aut], Dietmar Bauer [ctb]

Maintainer:

Lennart Oelschläger <oelschlaeger.lennart@gmail.com>

Repository:

CRAN

Date/Publication:

2025-10-21 11:30:07 UTC

ino: Initialization of Numerical Optimization

Description

Analysis of the initialization for numerical optimization of real-valued functions, particularly likelihood functions of statistical models. See https://loelschlaeger.de/ino/ for more details.

Author(s)

Maintainer: Lennart Oelschläger oelschlaeger.lennart@gmail.com (ORCID)

Authors:

Marius Ötting marius.oetting@uni-bielefeld.de (ORCID)

Other contributors:

Dietmar Bauer dietmar.bauer@uni-bielefeld.de [contributor]

Nop Object

Description

A Nop object defines a numerical optimization problem.

Getting started

Step 1: Create a `Nop` object

Call object <- Nop$new(f, target, npar, ...) where

f is the objective function,
target are the names of the target arguments,
npar specifies the lengths of the target arguments,
and ... are additional arguments for f.

You can now evaluate the objective function via the ⁠$evaluate()⁠ method.

Step 2: Specify numerical optimizers

Call ⁠object$set_optimizer(<optimizer object>)⁠, where ⁠<optimizer object>⁠ is an object of class optimizer, which can be created via the {optimizeR} package (please refer to the package homepage for details).

For example,

optimizeR::Optimizer$new(which = "stats::nlm") defines the nlm optimizer,
optimizeR::Optimizer$new(which = "stats::optim") defines the optim optimizer.

Step 3: Select initial values

Call initialization methods to define starting values for the optimization (the different initialization strategies are illustrated in the package vignettes), for example:

object$initialize_fixed() for fixed initial values,
object$initialize_random() for random initial values,
object$initialize_continue() for initial values based on parameter estimates from previous optimization runs.

Step 4: Optimization

Call object$optimize() for the optimization.

Step 5: Analyze the results

⁠$results⁠ returns a tibble of the optimization results,
⁠$optima()⁠ lists all identified optima,
⁠$minimum⁠ and ⁠$maximum⁠ return the best minimizer and maximizer

Progress during optimization

Displaying progress during multiple optimization runs via the {progressr} package is supported. To get started, run

progressr::handlers(global = TRUE)

and see handlers for details.

Parallel optimization

Parallel computation of multiple optimization runs via the {future} package is supported. To get started, run one of

future::plan(future::multisession)

and see plan for details.

Active bindings

initial_values

[list(), read-only]
The currently defined initial values.

Use the ⁠initialize_*()⁠ methods to add, transform, and reset values.

results

[tibble, read-only]
Optimization results with identifiers:

".optimization_label" (identifies the optimization run)
".optimizer_label" (identifies the optimizer)
".direction" (identifies the optimization direction)
".original" (identifies results obtained on the original problem)

The output has an associated autoplot method.

minimum

[list(2), read-only]
Best value and parameter across all (original) minimizations.

maximum

[list(2), read-only]
Best value and parameter across all (original) maximizations.

npar

[integer(), read-only]
The length of each target argument.

verbose

[logical(1)]
Print progress and details?

fresh_label

[character(1), read-only]
An optimization label that has not been used yet.

Methods

Public methods

Nop$new()
Nop$fixed_argument()
Nop$reduce_argument()
Nop$standardize_argument()
Nop$print()
Nop$evaluate()
Nop$set_optimizer()
Nop$initialize_fixed()
Nop$initialize_random()
Nop$initialize_grid()
Nop$initialize_custom()
Nop$initialize_continue()
Nop$initialize_filter()
Nop$initialize_promising()
Nop$initialize_transform()
Nop$initialize_reset()
Nop$optimize()
Nop$optima()
Nop$deviation()
Nop$clone()

Method `new()`

Creates a new Nop object.

The output has an associated autoplot method.

Usage

Nop$new(f, target = NULL, npar, gradient = NULL, hessian = NULL, ...)

Arguments

f

[function]
A function to be optimized (the so-called objective function).

It is expected that

f has at least one numeric argument,
the return value of f is of the structure numeric(1).

target

[character()]
The argument name(s) that get optimized (the so-called target arguments).

All target arguments must be numeric.

Can be NULL (default), then the first function argument is selected.

npar

[integer()]
The length of each target argument, i.e., the length(s) of the argument(s) specified via target.

gradient

[function | NULL]
Optionally a function that returns the gradient of f.

The function call of gradient must be identical to f.

Ignored for optimizers that do not support user-supplied gradient.

hessian

[function | NULL]
Optionally a function that returns the Hessian of f.

The function call of hessian must be identical to f.

Ignored for optimizers that do not support user-supplied Hessian.

...

Optionally additional function arguments passed to f (and gradient and hessian, if specified) that are fixed during the optimization.

Method `fixed_argument()`

Manages fixed arguments for the objective function.

Usage

Nop$fixed_argument(action, ...)

Arguments

action

[character(1)]
One of:

"set" to set an argument,
"get" to extract an argument value,
"remove" to remove an argument,
"reset" to reset an argument to its original value,
"modify" to modify an argument value.

Note that "set" overrides an argument value, while "modify" preserves the original value, which can be recovered via "reset".

...

Additional parameters depending on action:

named arguments if action = "set" or "modify",
a single argument name if action = "get", "remove", or "reset".

Method `reduce_argument()`

Reduces a fixed argument for the objective function.

Usage

Nop$reduce_argument(
  argument_name,
  proportion = 0.5,
  how = "random",
  centers = 2L,
  byrow = TRUE,
  ignore = integer()
)

Arguments

argument_name: [character(1)]
The name of a fixed argument for the objective function.
proportion, how, centers, byrow, ignore: Passed on to portion.

Method `standardize_argument()`

Standardizes a fixed argument for the objective function.

Usage

Nop$standardize_argument(
  argument_name,
  center = TRUE,
  scale = TRUE,
  byrow = FALSE,
  ignore = integer(),
  jointly = list()
)

Arguments

argument_name: [character(1)]
The name of a fixed argument for the objective function.
center, scale, byrow, ignore, jointly: Passed on to normalize.

Method `print()`

Prints details of the Nop object.

Usage

Nop$print(...)

Arguments

...: Currently not used.

Method `evaluate()`

Evaluates the objective function.

Usage

Nop$evaluate(
  at = rep(0, sum(self$npar)),
  .gradient_as_attribute = FALSE,
  .hessian_as_attribute = FALSE
)

Arguments

at

[numeric()]
The values for the target argument(s), written in a single vector.

Must be of length sum(self$npar).

.gradient_as_attribute, .hessian_as_attribute

[logical(1)]
Add gradient and / or Hessian value as attributes?

If gradient and / or Hessian function is not specified, numerical approximation is used.

Method `set_optimizer()`

Specifies a numerical optimizer.

Usage

Nop$set_optimizer(optimizer, optimizer_label = optimizer$label)

Arguments

optimizer: [Optimizer]
An Optimizer object, which can be created via Optimizer.
optimizer_label: [character(1)]
A (unique) label for the optimizer.

Method `initialize_fixed()`

Defines fixed initial values for the optimization.

Usage

Nop$initialize_fixed(at)

Arguments

at

[integer(self$sum(npar)) | list()]
The fixed initial parameter vector.

It can also be a list of such vectors.

Method `initialize_random()`

Defines random initial values for the optimization.

Usage

Nop$initialize_random(
  runs = 1L,
  sampler = function() stats::rnorm(sum(self$npar))
)

Arguments

runs: [integer(1)]
The number of optimization runs.
sampler: [function]
A function without any arguments that returns a numeric vector of length sum(self$npar).

Method `initialize_grid()`

Defines a grid of initial values for the optimization.

Usage

Nop$initialize_grid(lower = 0, upper = 1, breaks = 3, jitter = FALSE, ...)

Arguments

lower, upper: [numeric(1) | numeric(self$sum(npar))]
Lower and upper grid bounds for each parameter dimension.
breaks: [integer(1) | integer(self$sum(npar))]
The number of breaks for each parameter dimension.
jitter: Add noise to the grid points for a random grid layout?
...: Optional parameters passed to jitter.

Method `initialize_custom()`

Defines custom initial values for the optimization.

Usage

Nop$initialize_custom(at, seconds = rep(0, length(at)), type = "custom")

Arguments

at: [list()]
A list of initial parameter vectors.
seconds: [numeric(length(at))]
The number of seconds it took to obtain each initial value in at, which is added to the overall optimization time.
type: [character(1)]
The type of the initial values.

Method `initialize_continue()`

Defines initial values based on results from previous optimizations.

Usage

Nop$initialize_continue(optimization_label)

Arguments

optimization_label: [character(1)]
Label of optimization runs from which to select.

Method `initialize_filter()`

Filters initial values from the defined initial values.

Usage

Nop$initialize_filter(condition)

Arguments

condition

[character(1)]
Defines the condition on which the initial values are filtered, one of:

⁠"gradient_negative⁠ for points where the gradient is negative,
⁠"gradient_positive⁠ for points where the gradient is negative,
"hessian_negative" for points where the Hessian is negative definite,
"hessian_positive" for points where the Hessian is positive definite.

Method `initialize_promising()`

Selects promising initial values from the defined initial values.

Usage

Nop$initialize_promising(proportion, condition)

Arguments

proportion

[numeric(1)]
The proportion of selected from the defined initial values.

condition

[character(1)]
Defines the condition on which the initial values are selected, one of:

"value_small" for points where the function value is smallest,
"value_large" for points where the function value is largest,
"gradient_small" for points where the gradient norm is smallest,
"gradient_large" for points where the gradient norm is largest,
"condition_small" for points where the Hessian condition is smallest,
"condition_large" for points where the Hessian condition is largest.

Method `initialize_transform()`

Transforms the currently defined initial values.

Usage

Nop$initialize_transform(transformer = function(x) x)

Arguments

transformer: [⁠function()⁠]
A function that receives and returns a numeric() of length sum(self$npar).

Method `initialize_reset()`

Resets the currently defined initial values.

Usage

Nop$initialize_reset()

Method `optimize()`

Optimizes the target function.

Usage

Nop$optimize(
  optimization_label = self$fresh_label,
  which_optimizer = "all",
  which_direction = "min",
  lower = NULL,
  upper = NULL,
  seconds = Inf,
  hide_warnings = TRUE,
  reset_initial_afterwards = TRUE
)

Arguments

optimization_label

[character(1)]
A label for the optimization to distinguish optimization runs.

Setting a label is useful when using the ⁠$initialize_continue()⁠ method.

which_optimizer

[character() | integer()]
Selects numerical optimizers. Either:

"all" for all specified optimizers,
specific optimizer labels,
specified optimizer ids as defined in the print() output.

which_direction

[character()]
Selects the direction of optimization. One or both of:

"min" for minimization,
"max" for maximization.

lower, upper

[numeric() | NULL]
Optionally lower and upper parameter bounds.

Ignored for optimizers that do not support parameter bounds.

seconds

[numeric(1)]
A time limit in seconds.

Optimization is interrupted prematurely if seconds is exceeded.

Note the limitations documented in setTimeLimit.

hide_warnings

[logical(1)]
Hide any warnings during optimization?

reset_initial_afterwards

[logical(1)]
Reset the initial values after the optimization?

Details

Supports:

Parallel computation of multiple optimization runs via {future}
Progress messages via {progressr}

Method `optima()`

Lists all identified optima.

The output has an associated autoplot method.

Usage

Nop$optima(
  which_direction = "min",
  only_original = TRUE,
  group_by = NULL,
  sort_by_value = FALSE,
  digits = getOption("digits", default = 7)
)

Arguments

which_direction

[character()]
Selects the direction of optimization. One or both of:

"min" for minimization,
"max" for maximization.

only_original

['logical(1)]
Include only optima obtained on the original problem?

group_by

['character(1)]
Selects how the output is grouped. Either:

NULL to not group,
"optimization" to group by optimization label,
'"optimizer"“ to group by optimizer label.

sort_by_value

['logical(1)]
Sort by value? Else, sort by frequency.

digits

['integer(1)]
The number of decimal places.

Method `deviation()`

Compute deviations with respect to a reference parameter.

The output has an associated autoplot method.

Usage

Nop$deviation(
  reference = rep(0, sum(self$npar)),
  which_element = "initial",
  which_direction = "min",
  which_optimizer = "all",
  only_original = TRUE,
  parameter_labels = paste0("x", seq_len(sum(self$npar)))
)

Arguments

reference

[numeric()]
The reference vector of length sum(self$npar).

which_element

['character(1)]
Either

"initial" for deviations with respect to the initial values, or
"parameter" for deviations with respect to the estimated parameters.

which_direction

[character()]
Selects the direction of optimization. One or both of:

"min" for minimization,
"max" for maximization.

which_optimizer

[character() | integer()]
Selects numerical optimizers. Either:

"all" for all specified optimizers,
specific optimizer labels,
specified optimizer ids as defined in the print() output.

only_original

['logical(1)]
Include only optima obtained on the original problem?

parameter_labels

[character()]
Labels for the parameters of length sum(self$npar).

Method `clone()`

The objects of this class are cloneable with this method.

Usage

Nop$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

### define objective function, optimizer and initial values
Nop_ackley <- Nop$new(f = TestFunctions::TF_ackley, npar = 2)$
  set_optimizer(optimizeR::Optimizer$new(which = "stats::nlm"))$
  initialize_random(runs = 20)

### plot function surface and initial values
Nop_ackley |> ggplot2::autoplot()

### minimize objective function
Nop_ackley$optimize(which_direction = "min")

### show optima
Nop_ackley$optima(digits = 0)

### show best value and parameter across all minimizations
Nop_ackley$minimum

Example application to HMM likelihood

Description

This object is saved for reproducibility and to save computation time when building the vignettes.

See the vignette about the HMM likelihood for details on how this object was built: https://loelschlaeger.de/ino/articles/example_hmm.html

Usage

data("Nop_hmm")

Format

A Nop object.

Plotting methods

Description

autoplot.Nop() plots the objective function
autoplot.Nop_results() plots boxplots of optimization results
autoplot.Nop_optima() plots a bar chart of the found optima
autoplot.Nop_deviation() plots deviations per dimension from a reference

Usage

## S3 method for class 'Nop'
autoplot(object, xlim = NULL, xlim2 = NULL, ...)

## S3 method for class 'Nop_optima'
autoplot(object, ...)

## S3 method for class 'Nop_deviation'
autoplot(object, jitter = TRUE, ...)

## S3 method for class 'Nop_results'
autoplot(
  object,
  which_element = "seconds",
  group_by = NULL,
  relative = FALSE,
  ...
)

Arguments

object

Depends on the method:

for autoplot.Nop(), a Nop object
for autoplot.Nop_results(), the value Nop$results
for autoplot.Nop_optima(), the value Nop$optima
for autoplot.Nop_deviation(), the value Nop$deviation

xlim, xlim2

[numeric(2)]
Ranges for the first and second parameter to plot.

If NULL, they are derived from the specified initial values in object.

...

Other arguments passed to specific methods.

jitter

[logical(1)]
Apply jitter to the points?

which_element

[⁠character(1)\]\cr A column name of ⁠object' to plot.

group_by

['character(1)]
Selects how the plot is grouped. Either:

NULL to not group,
"optimization" to group by optimization label,
'"optimizer"“ to group by optimizer label.

relative

['logical(1)]
Plot values relative to the overall median?

Value

A ggplot object.

ino: Initialization of Numerical Optimization

Description

Author(s)

See Also

Nop Object

Description

Getting started

Step 1: Create a Nop object

Step 2: Specify numerical optimizers

Step 3: Select initial values

Step 4: Optimization

Step 5: Analyze the results

Progress during optimization

Parallel optimization

Active bindings

Methods

Public methods

Method new()

Usage

Arguments

Method fixed_argument()

Usage

Arguments

Method reduce_argument()

Usage

Arguments

Method standardize_argument()

Usage

Arguments

Method print()

Usage

Arguments

Method evaluate()

Usage

Arguments

Method set_optimizer()

Usage

Arguments

Method initialize_fixed()

Usage

Arguments

Method initialize_random()

Usage

Arguments

Method initialize_grid()

Usage

Arguments

Method initialize_custom()

Usage

Arguments

Method initialize_continue()

Usage

Arguments

Method initialize_filter()

Usage

Arguments

Method initialize_promising()

Usage

Arguments

Method initialize_transform()

Usage

Arguments

Method initialize_reset()

Usage

Method optimize()

Usage

Arguments

Details

Method optima()

Usage

Arguments

Method deviation()

Usage

Arguments

Method clone()

Usage

Arguments

Examples

Example application to HMM likelihood

Description

Step 1: Create a `Nop` object

Method `new()`

Method `fixed_argument()`

Method `reduce_argument()`

Method `standardize_argument()`

Method `print()`

Method `evaluate()`

Method `set_optimizer()`

Method `initialize_fixed()`

Method `initialize_random()`

Method `initialize_grid()`

Method `initialize_custom()`

Method `initialize_continue()`

Method `initialize_filter()`

Method `initialize_promising()`

Method `initialize_transform()`

Method `initialize_reset()`

Method `optimize()`

Method `optima()`

Method `deviation()`

Method `clone()`