Julia wrapper for the QOCO solver — a Quadratic Objective Conic Optimizer.

QOCO solves second-order cone programs (SOCPs) with quadratic objectives of the form:

min   (1/2)x'Px + c'x
s.t.  Ax = b
      Gx <=_C h

where C = R_+^l × SOC(q₁) × … × SOC(qₙ) is a product of the nonnegative orthant and second-order cones.

QOCO.jl is not currently registered in the Julia General registry, so install it directly from GitHub:

import Pkg
Pkg.add(url = "https://github.com/qoco-org/QOCO.jl.git")

This also installs the bundled QOCO_jll binaries, so you do not need to install QOCO separately.

using JuMP, QOCO

model = Model(QOCO.Optimizer)
set_silent(model)

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

optimize!(model)

value.(x)  # [0.5, 0.5]

import MathOptInterface as MOI

optimizer = QOCO.Optimizer()
MOI.set(optimizer, MOI.Silent(), true)

The QOCO optimizer supports the following native MathOptInterface objective functions and constraint types.

List of supported objective functions:

• MOI.ObjectiveFunction{MOI.VariableIndex}
• MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}
• MOI.ObjectiveFunction{MOI.ScalarQuadraticFunction{Float64}}

List of supported constraint types:

• MOI.VectorAffineFunction{Float64} in MOI.Zeros
• MOI.VectorAffineFunction{Float64} in MOI.Nonnegatives
• MOI.VectorAffineFunction{Float64} in MOI.SecondOrderCone

JuMP and MOI.Bridges.full_bridge_optimizer can bridge many scalar linear constraints and bound constraints into these native vector-affine forms.

QOCO is exposed as a one-shot, copy_to-based MOI optimizer. Incremental model construction is handled by JuMP or an MOI caching optimizer rather than by the native solver object itself.

The native interface supports quadratic objectives, but not quadratic constraints.

QOCO does not currently provide reliable infeasibility or unboundedness certificates through the wrapper, so such models may terminate with iteration or numerical-error statuses instead of MOI.INFEASIBLE or MOI.DUAL_INFEASIBLE.

QOCO does not support integer or mixed-integer optimization.

Settings can be passed as keyword arguments to the optimizer or set via MOI.RawOptimizerAttribute:

# Via constructor
optimizer = QOCO.Optimizer(; max_iters = 500, abstol = 1e-8)

# Via MOI
MOI.set(optimizer, MOI.RawOptimizerAttribute("max_iters"), 500)

MOI.Silent() takes precedence over the raw verbose setting. By default, the wrapper uses QOCO's compiled default (verbose = false). To enable solver output, set MOI.RawOptimizerAttribute("verbose") to true, or pass verbose = true to QOCO.Optimizer.