OptimizationExpression

Objective function or constraints

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Description

An OptimizationExpression is an arithmetic expression in terms of optimization variables for an objective function or for comparison in constraints.

Creation

Create an optimization expression by performing linear operations on OptimizationVariable objects. Use standard MATLAB® arithmetic, indexing, and concatenation of optimization variables to create expressions. See Examples.

You can also create an empty optimization expression by using optimexpr. Typically, you then fill the expression in a loop. For examples, see the optimexpr function reference page.

Properties

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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

Object Functions

evaluateEvaluate optimization expression
showexprDisplay optimization expression
writeexprSave optimization expression description

Examples

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Open Script

Create optimization expressions by arithmetic operations on optimization variables.

x = optimvar('x',3,2);
expr = sum(sum(x))

expr = 

  OptimizationExpression

    x(1, 1) + x(2, 1) + x(3, 1) + x(1, 2) + x(2, 2) + x(3, 2)


f = [2,10,4];
w = f*x;
showexpr(w)

(1, 1)

  2*x(1, 1) + 10*x(2, 1) + 4*x(3, 1)

(1, 2)

  2*x(1, 2) + 10*x(2, 2) + 4*x(3, 2)
Open Live Script

Create an optimization expression by transposing an optimization variable.

x = optimvar('x',3,2);
y = x'
y = 
  2×3 OptimizationExpression array with properties:

    IndexNames: {{}  {}}

  See expression formulation with showexpr.

Simply indexing into an optimization array does not create an expression, but instead creates an optimization variable that references the original variable. To see this, create a variable w that is the first and third row of x. Note that w is an optimization variable, not an optimization expression.

w = x([1,3],:)
w = 
  2×2 OptimizationVariable array with properties:

  Read-only array-wide properties:
          Name: 'x'
          Type: 'continuous'
      IsSubset: 1
    IndexNames: {{}  {}}

  Elementwise properties:
    LowerBound: [2×2 double]
    UpperBound: [2×2 double]

  Reference to a subset of OptimizationVariable with Name 'x'.

  See variables with showvar.
  See bounds with showbounds.

Create an optimization expression by concatenating optimization variables.

y = optimvar('y',4,3);
z = optimvar('z',4,7);
f = [y,z]
f = 
  4×10 OptimizationExpression array with properties:

    IndexNames: {{}  {}}

  See expression formulation with showexpr.
Open Script

Use optimexpr to create an empty expression, then fill the expression in a loop.

y = optimvar('y',6,4);
expr = optimexpr(3,2);
for i = 1:3
    for j = 1:2
        expr(i,j) = y(2*i,j) - y(i,2*j);
    end
end
showexpr(expr)

(1, 1)

  y(2, 1) - y(1, 2)

(2, 1)

  y(4, 1) - y(2, 2)

(3, 1)

  y(6, 1) - y(3, 2)

(1, 2)

  y(2, 2) - y(1, 4)

(2, 2)

  y(4, 2) - y(2, 4)

(3, 2)

  y(6, 2) - y(3, 4)

Definitions

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See Also

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Topics

Introduced in R2017b

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