JuMP 1.15.0 is released

We are happy to announce the release of JuMP 1.15.0.

This is a very large minor release because it adds an entirely new data structure and API path for working with nonlinear programs.

The previous nonlinear interface remains unchanged and is documented at Nonlinear Modeling (Legacy). The new interface is a treated as a non-breaking feature addition and is documented at Nonlinear Modeling.


The “legacy” nonlinear interface was some of the oldest code in JuMP. When we created MathOptInterface (and rewrote nearly all of JuMP), we explicitly decided to leave the nonlinear interface as it was, and “come back to it later.”

Over the years, the limitations of JuMP’s nonlinear interface have been a constant source of frustration for users. Why could you only create nonlinear expressions in the @NL macros? Why were the @NLconstraint and @NLobjective macros needed instead of the normal @constraint and @objective? Why could you not use sum(::Vector) or compute a dot product inside a nonlinear macro? The discourse forum is filled with questions, hacks, and work-arounds for all things related to nonlinear programming.

Two years ago, and motivated by this public demand, we received funding from Los Alamos National Laboratory to begin a rewrite of JuMP’s nonlinear interface with the goal of bringing first-class nonlinear support to JuMP. This release is the culmination of that work.


Here are some highlights of the new features.

Operator overloading

Nonlinear expressions can be defined outside of macros like their quadratic and affine counterparts:

julia> using JuMP

julia> model = Model();

julia> @variable(model, x);

julia> expr = x^2.3 + sin(x)
(x ^ 2.3) + sin(x)

julia> typeof(expr)
NonlinearExpr (alias for GenericNonlinearExpr{GenericVariableRef{Float64}})

julia> expr.head

julia> expr.args
2-element Vector{Any}:
 x ^ 2.3

Macro definitions

We can define nonlinear expressions inside of @expression, @objective, and @constraint. The special @NL macros are no longer required.

julia> @expression(model, x + x^3 * sin(x)^x)
x + ((x ^ 3) * (sin(x) ^ x))

LinearAlgebra support

We can also do linear algebra operations:

julia> @variable(model, X[1:3, 1:2]);

julia> @variable(model, v[1:3]);

julia> @variable(model, w[1:2]);

julia> @expression(model, v' * X * w)
0.0 + ((X[1,1]*v[1] + X[2,1]*v[2] + X[3,1]*v[3]) * w[1]) + ((X[1,2]*v[1] + X[2,2]*v[2] + X[3,2]*v[3]) * w[2])

including broadcasting:

julia> @variable(model, Z[1:2, 1:2], Symmetric);

julia> @objective(model, Min, sum(Z^4 .- Z.^3))
0.0 + (((+(0.0) + (((+(0.0) + ((Z[1,2]) * (Z[1,1]))) + ...
# ... long expression not shown ...

Function tracing

Because we support operator overloading, calling a regular Julia function with JuMP variables produces a nonnlinear expression:

julia> my_func(y) = 2^y + exp(y^-2.3);

julia> my_func(2.0)

julia> my_func(x)
(2.0 ^ x) + exp(x ^ -2.3)

Function tracing should greatly simplify a number of nonlinear models. For example, the model in this Discourse thread becomes:

using JuMP, Ipopt
function example()
    Q = -0.8:0.4:0.8
    model = Model(Ipopt.Optimizer)
    @variable(model, -2 <= p[1:5] <= 2)
    @variable(model, -1 <= w <= 3)
    @variable(model, -1 <= q <= 3)
    @objective(model, Min, w)
    f(p, q) = (1 / sqrt(2π)) * exp(-((p - q)^2) / 2)
    total(p, q) = sum(_p * f(i, q) for (i, _p) in enumerate(p))
    l1(p, q) = 1 - total(p, q) + 0.5 * total(p, 0.5)
    l2(p, q) = total(p, q) - 1
    lhs(p, q, _q) = l1(p, q) - l1(p, _q)
    @constraint(model, [_q in Q], w * lhs(p, q, _q) + (1 - w) * l2(p, q) <= 0)

User-defined operators

To prevent tracing, you can create an operator instead:

julia> my_func2(a) = sin(a) * eta(a);

julia> @operator(model, op_my_func, 1, my_func2)
NonlinearOperator(my_func2, :op_my_func)

julia> @expression(model, op_my_func(x)^2)
op_my_func(x) ^ 2.0

Vector-valued nonlinear functions

We now support multi-objective programs with nonlinear objectives:

julia> model = Model();

julia> @variable(model, x[1:4]);

julia> @objective(model, Min, [sum(abs.(x)), sqrt(sum(x.^2))])
2-element Vector{NonlinearExpr}:
 (((+(0.0) + abs(x[1])) + abs(x[2])) + abs(x[3])) + abs(x[4])
 sqrt(x[1]² + x[2]² + x[3]² + x[4]²)

and we support nonlinear mixed complementarity problems

julia> model = Model();

julia> @variable(model, x >= 0);

julia> @constraint(model, log(x + 0.1)  x)
[log(x + 0.1), +(x)]  MathOptInterface.Complements(2)

Potential breaking changes

Although the new nonlinear interface is a feature addition, there are two changes which might be breaking for a very small number of users.

Next steps

Try it out! If you encounter any problems, or have any feedback on the new interface, please start a discourse thread or open a Github issue.