# 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:** 15

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**Author:** ![geoffroyleconte](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/geoffroyleconte/32/21661_2.png) [@geoffroyleconte](https://discourse.julialang.org/u/geoffroyleconte)\
**Post date:** [March 5, 2024, 11:24pm UTC](https://discourse.julialang.org/t/how-to-solve-a-large-quadratic-programming-problem/111200/15 "2024-03-05T23:24:51Z")

</div>

To complete @dpo’s answer and to conform with the notations of [Reference · QuadraticModels.jl](https://jso.dev/QuadraticModels.jl/stable/reference/#QuadraticModels.QuadraticModel) , I think your problem can be written as

\min\_x \tfrac{1}{2}x^THx \quad \text{s.t.} \quad Ax = b, \quad \text{and} \quad x\_i \ge 0, \quad i=1, ..., n,

where

x = \begin{bmatrix} f \\ r \end{bmatrix}, H = \begin{bmatrix} 2 \alpha I & 0 \\ 0 & I \end{bmatrix}, A = \begin{bmatrix} K & I \end{bmatrix}, b = g, and f \in \mathbb{R}^n

Then, a small example with RipQP.jl would give

```julia
using RipQP, QuadraticModels, LinearAlgebra, SparseArrays
m, n = 30, 100
K = rand(m, n)
α = 1.0
g = rand(m)
A = [sparse(K) I]
H = [2*α*I spzeros(n, m);
     spzeros(m, n) 2*I]
c = zeros(m + n)
lvar = [zeros(n); fill(-Inf, m)]
qm = QuadraticModel(c, H; A = A, lcon = g, ucon = g, lvar = lvar)
stats = ripqp(qm)
f, r = stats.solution[1:n], stats.solution[n+1:n+m]

```

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