Documentation

optimvar

Create optimization variables

Description

example

x = optimvar(name) creates a scalar optimization variable. An optimization variable is a symbolic object that enables you to create expressions for the objective function and the problem constraints in terms of the variable.

Tip

To avoid confusion, set name to be the MATLAB® variable name. For example,

metal = optimvar('metal')

example

x = optimvar(name,n) creates an n-by-1 vector of optimization variables.

example

x = optimvar(name,cstr) creates a vector of optimization variables that can use cstr for indexing. The number of elements of x is the same as the length of the cstr vector. The orientation of x is the same as the orientation of cstr: x is a row vector when cstr is a row vector, and x is a column vector when cstr is a column vector.

example

x = optimvar(name,cstr1,n2,...,cstrk) or x = optimvar(name,{cstr1,cstr2,...,cstrk}) or x = optimvar(name,[n1,n2,...,nk]), for any combination of positive integers nj and names cstrk, creates an array of optimization variables with dimensions equal to the integers nj and the lengths of the entries cstr1k.

example

x = optimvar(___,Name,Value), for any previous syntax, uses additional options specified by one or more Name,Value pair arguments. For example, to specify an integer variable, use x = optimvar('x','Type','integer').

Examples

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Create a scalar optimization variable named dollars.

dollars = optimvar('dollars')
dollars =
OptimizationVariable with properties:

Name: 'dollars'
Type: 'continuous'
IndexNames: {{}  {}}
LowerBound: -Inf
UpperBound: Inf

See variables with show.
See bounds with showbounds.

Create a 3-by-1 optimization variable vector named x.

x = optimvar('x',3)
x =
3x1 OptimizationVariable array with properties:

Array-wide properties:
Name: 'x'
Type: 'continuous'
IndexNames: {{}  {}}

Elementwise properties:
LowerBound: [3x1 double]
UpperBound: [3x1 double]

See variables with show.
See bounds with showbounds.

Create an integer optimization variable vector named bolts that is indexed by the strings "brass", "stainless", and "galvanized". Use the indices of bolts to create an optimization expression, and experiment with creating bolts using character arrays or in a different orientation.

Create bolts using strings in a row orientation.

bnames = ["brass","stainless","galvanized"];
bolts = optimvar('bolts',bnames,'Type','integer')
bolts =
1x3 OptimizationVariable array with properties:

Array-wide properties:
Name: 'bolts'
Type: 'integer'
IndexNames: {{}  {1x3 cell}}

Elementwise properties:
LowerBound: [-Inf -Inf -Inf]
UpperBound: [Inf Inf Inf]

See variables with show.
See bounds with showbounds.

Create an optimization expression using the string indices.

y = bolts("brass") + 2*bolts("stainless") + 4*bolts("galvanized")
y =
Linear OptimizationExpression

bolts('brass') + 2*bolts('stainless') + 4*bolts('galvanized')

Use a cell array of character vectors instead of strings to get a variable with the same indices as before.

bnames = {'brass','stainless','galvanized'};
bolts = optimvar('bolts',bnames,'Type','integer')
bolts =
1x3 OptimizationVariable array with properties:

Array-wide properties:
Name: 'bolts'
Type: 'integer'
IndexNames: {{}  {1x3 cell}}

Elementwise properties:
LowerBound: [-Inf -Inf -Inf]
UpperBound: [Inf Inf Inf]

See variables with show.
See bounds with showbounds.

Use a column-oriented version of bnames, 3-by-1 instead of 1-by-3, and observe that bolts has that orientation as well.

bnames = ["brass";"stainless";"galvanized"];
bolts = optimvar('bolts',bnames,'Type','integer')
bolts =
3x1 OptimizationVariable array with properties:

Array-wide properties:
Name: 'bolts'
Type: 'integer'
IndexNames: {{1x3 cell}  {}}

Elementwise properties:
LowerBound: [3x1 double]
UpperBound: [3x1 double]

See variables with show.
See bounds with showbounds.

Create a 3-by-4-by-2 array of optimization variables named xarray.

xarray = optimvar('xarray',3,4,2)
xarray =
3x4x2 OptimizationVariable array with properties:

Array-wide properties:
Name: 'xarray'
Type: 'continuous'
IndexNames: {{}  {}  {}}

Elementwise properties:
LowerBound: [3x4x2 double]
UpperBound: [3x4x2 double]

See variables with show.
See bounds with showbounds.

You can also create multidimensional variables indexed by a mixture of names and numeric indices. For example, create a 3-by-4 array of optimization variables where the first dimension is indexed by the strings 'brass', 'stainless', and 'galvanized', and the second dimension is numerically indexed.

bnames = ["brass","stainless","galvanized"];
bolts = optimvar('bolts',bnames,4)
bolts =
3x4 OptimizationVariable array with properties:

Array-wide properties:
Name: 'bolts'
Type: 'continuous'
IndexNames: {{1x3 cell}  {}}

Elementwise properties:
LowerBound: [3x4 double]
UpperBound: [3x4 double]

See variables with show.
See bounds with showbounds.

Create an optimization variable named x of size 3-by-3-by-3 that represents binary variables.

x = optimvar('x',3,3,3,'Type','integer','LowerBound',0,'UpperBound',1)
x =
3x3x3 OptimizationVariable array with properties:

Array-wide properties:
Name: 'x'
Type: 'integer'
IndexNames: {{}  {}  {}}

Elementwise properties:
LowerBound: [3x3x3 double]
UpperBound: [3x3x3 double]

See variables with show.
See bounds with showbounds.

Input Arguments

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Variable name, specified as a character vector or string.

Tip

To avoid confusion about which name relates to which aspect of a variable, set the workspace variable name to the variable name. For example,

truck = optimvar('truck');

Example: "Warehouse"

Example: 'truck'

Data Types: char | string

Variable dimension, specified as a positive integer.

Example: 4

Data Types: double

Index names, specified as a string array or a cell array of character arrays.

Example: x = optimvar('x',["Warehouse","Truck","City"])

Example: x = optimvar('x',{'Warehouse','Truck','City'})

Data Types: string | cell

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: Create x as a 3-element nonnegative vector with x(2) <= 2 and x(3) <= 4 by the command x = optimvar('x',3,'LowerBound',0,'UpperBound',[Inf,2,4])

Variable type, specified as 'continuous' or 'integer'.

• 'continuous' – Real values

• 'integer' – Integer values

The variable type applies to all variables in the array. To have multiple variable types, create multiple variables.

Tip

To specify binary variables, use the 'integer' type with LowerBound equal to 0 and UpperBound equal to 1.

Example: 'integer'

Lower bounds, specified as an array of the same size as x or as a real scalar. If LowerBound is a scalar, the value applies to all elements of x.

Example: To set a lower bound of 0 to all elements of x, specify the scalar value 0.

Data Types: double

Upper bounds, specified as an array of the same size as x or as a real scalar. If UpperBound is a scalar, the value applies to all elements of x.

Example: To set an upper bound of 2 to all elements of x, specify the scalar value 2.

Data Types: double

Output Arguments

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Optimization variable, returned as an OptimizationVariable array. The dimensions of the array are the same as those of the corresponding input variables, such as cstr1-by-cstr2.

Tips

• OptimizationVariable objects have handle copy behavior. See Handle Object Behavior (MATLAB) and Comparison of Handle and Value Classes (MATLAB). Handle copy behavior means that a copy of an OptimizationVariable points to the original and does not have an independent existence. For example, create a variable x, copy it to y, then set a property of y. Note that x takes on the new property value.

x = optimvar('x','LowerBound',1);
y = x;
y.LowerBound = 0;
showbounds(x)
0 <= x

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