# Objectives

More information can be found in the Objectives section of the manual.

## Objective functions

JuMP.@objectiveMacro
@objective(model::Model, sense, func)

Set the objective sense to sense and objective function to func. The objective sense can be either Min, Max, MathOptInterface.MIN_SENSE, MathOptInterface.MAX_SENSE or MathOptInterface.FEASIBILITY_SENSE; see MathOptInterface.ObjectiveSense. In order to set the sense programmatically, i.e., when sense is a Julia variable whose value is the sense, one of the three MathOptInterface.ObjectiveSense values should be used. The function func can be a single JuMP variable, an affine expression of JuMP variables or a quadratic expression of JuMP variables.

Examples

To minimize the value of the variable x, do as follows:

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> @variable(model, x)
x

julia> @objective(model, Min, x)
x

To maximize the value of the affine expression 2x - 1, do as follows:

julia> @objective(model, Max, 2x - 1)
2 x - 1

To set a quadratic objective and set the objective sense programmatically, do as follows:

julia> sense = MOI.MIN_SENSE
MIN_SENSE::OptimizationSense = 0

julia> @objective(model, sense, x^2 - 2x + 1)
x² - 2 x + 1
source
JuMP.objective_functionFunction
objective_function(model::Model,
T::Type{<:AbstractJuMPScalar}=objective_function_type(model))

Return an object of type T representing the objective function. Error if the objective is not convertible to type T.

Examples

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> @variable(model, x)
x

julia> @objective(model, Min, 2x + 1)
2 x + 1

julia> objective_function(model, AffExpr)
2 x + 1

2 x + 1

GenericQuadExpr{Float64,VariableRef}

We see with the last two commands that even if the objective function is affine, as it is convertible to a quadratic function, it can be queried as a quadratic function and the result is quadratic.

However, it is not convertible to a variable.

julia> objective_function(model, VariableRef)
ERROR: InexactError: convert(MathOptInterface.SingleVariable, MathOptInterface.ScalarAffineFunction{Float64}(MathOptInterface.ScalarAffineTerm{Float64}[MathOptInterface.ScalarAffineTerm{Float64}(2.0, MathOptInterface.VariableIndex(1))], 1.0))
[...]
source
JuMP.set_objective_coefficientFunction
set_objective_coefficient(model::Model, variable::VariableRef, coefficient::Real)

Set the linear objective coefficient associated with Variable to coefficient.

Note: this function will throw an error if a nonlinear objective is set.

source
JuMP.set_objectiveFunction
set_objective(model::AbstractModel, sense::MOI.OptimizationSense, func)

The functional equivalent of the @objective macro.

Sets the objective sense and objective function simultaneously, and is equivalent to:

set_objective_sense(model, sense)
set_objective_function(model, func)

Examples

model = Model()
@variable(model, x)
set_objective(model, MOI.MIN_SENSE, x)
source