# 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:** 11

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**Author:** ![dpo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpo/32/3335_2.png) [@dpo](https://discourse.julialang.org/u/dpo)\
**Post date:** [March 5, 2024, 8:30pm UTC](https://discourse.julialang.org/t/how-to-solve-a-large-quadratic-programming-problem/111200/11 "2024-03-05T20:30:55Z")

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Interior-point methods would be very well suited for this kind of problem. We call it a bound-constrained linear least-squares problem. An easy way to solve it is to rewrite it as

\begin{align\*} \min\_{f,r} & \ \|r\|^2 + \alpha \|f\|^2 \\ \mathrm{subject \ to} & \ Kf + r = g \\ & f \geq 0. \end{align\*}

That formulation will avoid any occurrence of K^T K, which could be dense and ill conditioned.

The problem can be solved using [RipQP](https://github.com/JuliaSmoothOptimizers/RipQP.jl).

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