OptimizationVariable
Variable for optimization
Description
An OptimizationVariable
object contains variables for
optimization expressions. Use expressions to represent an objective function,
constraints, or equations. Variables are symbolic in nature, and can be arrays of any
size.
Tip
For the full workflow, see Problem-Based Optimization Workflow or Problem-Based Workflow for Solving Equations.
Creation
Create an OptimizationVariable
object using optimvar
.
Properties
Array-Wide Properties
Name
— Variable name
string | character vector
This property is read-only.
Variable name, specified as a string or character vector.
Name
gives the variable label to be displayed, such as
in show
or write
. Name
also gives the field names in
the solution structure that solve
returns.
Tip
To avoid confusion, set name
to be the MATLAB® variable name. For example,
metal = optimvar('metal')
Data Types: char
| string
Type
— Variable type
'continuous'
(default) | 'integer'
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 a binary variable, use the 'integer'
type and specify LowerBound
= 0
and UpperBound
= 1
.
Data Types: char
| string
IndexNames
— Index names
''
(default) | cell array of strings | cell array of character vectors
Index names, specified as a cell array of strings or character vectors. For information on using index names, see Named Index for Optimization Variables.
Data Types: cell
Element-wise Properties
LowerBound
— Lower bound
-Inf
(default) | real scalar | real array
Lower bound, specified as a real scalar or as a real array having the same
dimensions as the OptimizationVariable
object. Scalar
values apply to all elements of the variable.
The LowerBound
property is always displayed as an
array. However, you can set the property as a scalar that applies to all
elements. For example,
var.LowerBound = 0
Data Types: double
UpperBound
— Upper bound
Inf
(default) | real scalar | real array
Upper bound, specified as a real scalar or as a real array having the same
dimensions as the OptimizationVariable
object. Scalar
values apply to all elements of the variable.
The UpperBound
property is always displayed as an
array. However, you can set the property as a scalar that applies to all
elements. For example
var.UpperBound = 1
Data Types: double
Object Functions
show | Display information about optimization object |
showbounds | Display variable bounds |
write | Save optimization object description |
writebounds | Save description of variable bounds |
Examples
Create Scalar Optimization Variable
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 Optimization Variable Vector
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 Optimization Variables Indexed by Strings
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: {{} {1x2 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: {{} {1x2 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: {{1x2 cell} {}} Elementwise properties: LowerBound: [3x1 double] UpperBound: [3x1 double] See variables with show. See bounds with showbounds.
Create Multidimensional Optimization Variables
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: {{1x2 cell} {}} Elementwise properties: LowerBound: [3x4 double] UpperBound: [3x4 double] See variables with show. See bounds with showbounds.
Create Binary Optimization Variables
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.
More About
Arithmetic Operations
For the list of supported operations on optimization variables, see Supported Operations for Optimization Variables and Expressions.
Reference
An optimization variable reference is an optimization variable that is a subset of another optimization variable. The reference variable points to, meaning it is an alias of, the original variable. The reference variable does not have an independent existence.
For example, suppose x
is a 3-element optimization
variable:
x = optimvar('x',3,1);
Take y
as the last two elements of x
.
y = x(2:3);
Then y(1)
is an alias of x(2)
, and
y(2)
is an alias of x(3)
. If you use
y
in an optimization expression, the expression includes
x
, not y
. For example,
expr = [1,2]*y
expr = OptimizationExpression x(2) + 2*x(3)
Furthermore, any modification of y
produces a modification of
x
. For example,
y.LowerBound = 2; showbounds(x)
2 <= x(2, 1) 2 <= x(3, 1)
Tips
OptimizationVariable
objects have handle copy behavior. See Handle Object Behavior and Comparison of Handle and Value Classes. Handle copy behavior means that a copy of anOptimizationVariable
points to the original and does not have an independent existence. For example, create a variablex
, copy it toy
, then set a property ofy
. Note thatx
takes on the new property value.x = optimvar('x','LowerBound',1); y = x; y.LowerBound = 0; showbounds(x)
0 <= x
Version History
Introduced in R2017bR2024a: Create optimization variables using the "like"
syntax
You can create optimization variables using the "like"
syntax.
This capability can simplify the initialization of optimization expressions, as
shown in Use "like" Syntax to Initialize the Array.
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