# How to solve a large quadratic programming problem

**URL:** <https://discourse.julialang.org/t/how-to-solve-a-large-quadratic-programming-problem/111200>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization, nonlinear\
**Created:** [March 5, 2024, 3:20pm UTC](https://discourse.julialang.org/t/how-to-solve-a-large-quadratic-programming-problem/111200 "2024-03-05T15:20:31Z")\
**Posts on this page:** 1\
**Showing post:** 10

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**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 5, 2024, 8:15pm UTC](https://discourse.julialang.org/t/how-to-solve-a-large-quadratic-programming-problem/111200/10 "2024-03-05T20:15:03Z")

</div>

The JuMP approach would be something like this:

```julia
using JuMP, SCS

function main(K, g, α)
    model = Model(SCS.Optimizer)
    @variable(model, f[1:size(K, 2)] >= 0)
    @variable(model, t[1:2])
    @constraint(model, [t[1]; 0.5; g - K * f] in RotatedSecondOrderCone())
    @constraint(model, [t[2]; 0.5; f] in RotatedSecondOrderCone())
    @objective(model, Min, t[1] + α * t[2])
    optimize!(model)
    @assert is_solved_and_feasible(model)
    return value.(f)
end

m, n = 300, 10_000
K = rand(m, n);
g = rand(m);
α = 0.5
main(K, g, α)

```

See the docs:

- [Constraints · JuMP](https://jump.dev/JuMP.jl/stable/manual/constraints/#Rotated-second-order-cone-constraints)
- [Tips and Tricks · JuMP](https://jump.dev/JuMP.jl/stable/tutorials/conic/tips_and_tricks/#Rotated-Second-Order-Cone)

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