# Suggestions on model and solvers
**URL:** https://discourse.julialang.org/t/suggestions-on-model-and-solvers/79345
**Category:** Optimization (Mathematical)
**Created:** [April 11, 2022, 2:33pm UTC](https://discourse.julialang.org/t/suggestions-on-model-and-solvers/79345 "2022-04-11T14:33:14Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Patrik\_Waldmann](https://discourse.julialang.org/u/Patrik_Waldmann)
#### Post date: [April 11, 2022, 2:33pm UTC](https://discourse.julialang.org/t/suggestions-on-model-and-solvers/79345/1 "2022-04-11T14:33:14Z")
I would be happy for suggestions on how and where to implement the model for the data below (the plan is to extend to a much larger data set later so speed is of interest):
```julia
#Toy data
A = [1.0000 0 0.5000 0.5000 0.4714 0.2357;
0 1.0000 0.5000 0 0.2357 0.5893;
0.5000 0 0.2500 1.0000 0.5893 0.2946;
0.5000 0 0.2500 1.0000 0.5893 0.2946;
0.4714 0.2357 0.5893 0.5893 1.0000 0.6111;
0.2357 0.5893 0.5303 0.2946 0.6111 1.0000]
g = [0.5 -0.2 0.3 0.2 0.0 -0.1]
s = [1 0 1 1 0 0]
d = [0 1 0 0 1 1]
F = 0.3
#Model
max c'*g
constr c'*A*c/2 ≤ F
c'*s = 0.5
c'*d = 0.5
c ≥ 0
```
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [April 11, 2022, 2:45pm UTC](https://discourse.julialang.org/t/suggestions-on-model-and-solvers/79345/2 "2022-04-11T14:45:13Z")
If your decision variable is indeed `c`, then this looks like a [Quadratic Program (QP)](https://en.wikipedia.org/wiki/Quadratic_programming).
I would try my luck with [JuMP.jl](https://jump.dev/JuMP.jl/stable/) (see nonlinear modeling examples such as [this one](https://jump.dev/JuMP.jl/stable/tutorials/nonlinear/portfolio/)). You will need to select an appropriate solver from [this list](https://jump.dev/JuMP.jl/stable/installation/#Supported-solvers), i.e. one that supports QP.
---
### Author:  [@mtanneau](https://discourse.julialang.org/u/mtanneau)
#### Post date: [April 11, 2022, 11:30pm UTC](https://discourse.julialang.org/t/suggestions-on-model-and-solvers/79345/3 "2022-04-11T23:30:59Z")
The objective `c'*g` is linear, and the constraint `c'*A*c/2 ≤ F` is quadratic, so this is a quadratically-constrained problem, not linearly-constrained QP. The corresponding example in the JuMP doc would be [this one](https://jump.dev/JuMP.jl/stable/tutorials/nonlinear/qcp/).
If `A` is symmetric positive semi-definite, then the problem is convex and solvable fairly efficiently by several solvers such as Ipopt, CPLEX, Gurobi, Xpress, etc.
If `A` is _not_ symmetric positive semi-definite, then the problem is non convex (and much more difficult to solve exactly). In that situation, Ipopt should give decent solution, though no guarantee of feasibility / optimality. Gurobi can solve non-convex QCPs to global optimality, potentially taking some time if the problem is large.
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [April 12, 2022, 4:47am UTC](https://discourse.julialang.org/t/suggestions-on-model-and-solvers/79345/4 "2022-04-12T04:47:36Z")
My bad I had switched the objective and constraints ^^ Edited my answer