JuMP Integration

ConicIP provides a MathOptInterface wrapper, so it can be used as a solver backend for JuMP.

Setup

using JuMP, ConicIP
model = Model(ConicIP.Optimizer)

Solver Options

Pass options at construction via an anonymous function:

model = Model(() -> ConicIP.Optimizer(verbose=false, optTol=1e-8, maxIters=200))

The available options are:

Option	Type	Default	Description
`verbose`	`Bool`	`false`	Print solver iterations
`optTol`	`Float64`	`1e-6`	Optimality tolerance
`maxIters`	`Int`	`100`	Maximum iterations

Example: Simple LP

using JuMP, ConicIP

model = Model(() -> ConicIP.Optimizer(verbose=false, optTol=1e-6))

@variable(model, x[1:2] >= 0)
@objective(model, Min, x[1] + x[2])
@constraint(model, x[1] + x[2] >= 1)

optimize!(model)
termination_status(model)

OPTIMAL::TerminationStatusCode = 1

round(objective_value(model), digits=6)

1.0

Example: SOC Constraint

using JuMP, ConicIP

model = Model(() -> ConicIP.Optimizer(verbose=false, optTol=1e-6))

@variable(model, x[1:2])
@variable(model, t)
@objective(model, Min, t)
@constraint(model, x[1] == 1)
@constraint(model, x[2] == 1)
@constraint(model, [t; x] in SecondOrderCone())

optimize!(model)
termination_status(model)

OPTIMAL::TerminationStatusCode = 1

The minimum norm is √2:

round(objective_value(model), digits=4)

1.4142

Example: Maximization

using JuMP, ConicIP

model = Model(() -> ConicIP.Optimizer(verbose=false, optTol=1e-6))

@variable(model, x[1:2] >= 0)
@objective(model, Max, x[1] + 2x[2])
@constraint(model, x[1] + x[2] <= 1)

optimize!(model)
termination_status(model)

OPTIMAL::TerminationStatusCode = 1

round(objective_value(model), digits=6)

2.0

Supported Constraints

Constraint type	JuMP syntax
Nonnegative	`@variable(model, x >= 0)` or `@constraint(model, x in MOI.Nonnegatives(n))`
Nonpositive	`@constraint(model, x in MOI.Nonpositives(n))`
Zero (equality)	`@constraint(model, x .== 0)` or `@constraint(model, x in MOI.Zeros(n))`
Second-order cone	`@constraint(model, [t; x] in SecondOrderCone())`
PSD (experimental)	`@constraint(model, X in PSDCone())`
Scalar equal	`@constraint(model, x == 1)`
Scalar greater	`@constraint(model, x >= 1)`
Scalar less	`@constraint(model, x <= 1)`

Limitations

No quadratic objectives through JuMP

The MOI wrapper currently supports only linear objectives. For quadratic programs, use the direct conicIP interface.

Other limitations:

No integer variables
No indicator or SOS constraints
Semidefinite support is experimental