Objective

This page describes macros and functions related to linear and quadratic objective functions only, unless otherwise indicated. For nonlinear objective functions, see Nonlinear Modeling.

Use the @objective macro to set linear and quadratic objective functions in a JuMP model. The functions set_objective_sense and set_objective_function provide an equivalent lower-level interface.

To query the objective function from a model, see objective_sense, objective_function, and objective_function_type.

To query the optimal objective value or best known bound after a solve, see objective_value and objective_bound. These two functions apply to nonlinear objectives also.

Reference

JuMP.@objective — Macro.

@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 programatically, 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 programatically, do as follows:

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

julia> @objective(model, sense, x^2 - 2x + 1)
x² - 2 x + 1

JuMP.set_objective_sense — Function.

set_objective_sense(model::Model, sense::MathOptInterface.OptimizationSense)

Sets the objective sense of the model to the given sense. See set_objective_function to set the objective function. These are low-level functions; the recommended way to set the objective is with the @objective macro.

JuMP.set_objective_function — Function.

set_objective_function(
    model::Model,
    func::Union{AbstractJuMPScalar, MathOptInterface.AbstractScalarFunction})

Sets the objective function of the model to the given function. See set_objective_sense to set the objective sense. These are low-level functions; the recommended way to set the objective is with the @objective macro.

JuMP.objective_sense — Function.

objective_sense(model::Model)::MathOptInterface.OptimizationSense

Return the objective sense.

JuMP.objective_function — Function.

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

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

julia> typeof(objective_function(model, QuadExpr))
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}[ScalarAffineTerm{Float64}(2.0, VariableIndex(1))], 1.0))
Stacktrace:
 [1] convert at /home/blegat/.julia/dev/MathOptInterface/src/functions.jl:398 [inlined]
 [2] get(::JuMP.JuMPMOIModel{Float64}, ::MathOptInterface.ObjectiveFunction{MathOptInterface.SingleVariable}) at /home/blegat/.julia/dev/MathOptInterface/src/Utilities/model.jl:290
 [3] get at /home/blegat/.julia/dev/MathOptInterface/src/Utilities/universalfallback.jl:114 [inlined]
 [4] get at /home/blegat/.julia/dev/MathOptInterface/src/Utilities/cachingoptimizer.jl:439 [inlined]
 [5] get(::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.AbstractOptimizer,MathOptInterface.Utilities.UniversalFallback{JuMP.JuMPMOIModel{Float64}}},MathOptInterface.Bridges.AllBridgedConstraints{Float64}}, ::MathOptInterface.ObjectiveFunction{MathOptInterface.SingleVariable}) at /home/blegat/.julia/dev/MathOptInterface/src/Bridges/bridgeoptimizer.jl:172
 [6] objective_function(::Model, ::Type{VariableRef}) at /home/blegat/.julia/dev/JuMP/src/objective.jl:129
 [7] top-level scope at none:0

JuMP.objective_function_type — Function.

objective_function_type(model::Model)::AbstractJuMPScalar

Return the type of the objective function.

JuMP.objective_bound — Function.

objective_bound(model::Model)

Return the best known bound on the optimal objective value after a call to optimize!(model).

JuMP.objective_value — Function.

objective_value(model::Model)

Return the objective value after a call to optimize!(model).