# Quadratic Programming Problem - CPL

**URL:** <https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization\
**Created:** [February 22, 2019, 7:40am UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068 "2019-02-22T07:40:27Z")\
**Posts on this page:** 10\
**Page:** 1

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**Author:** ![Rajat\_Sanyal](https://avatars.discourse-cdn.com/v4/letter/r/4da419/32.png) [@Rajat\_Sanyal](https://discourse.julialang.org/u/Rajat_Sanyal)\
**Post date:** [February 22, 2019, 7:40am UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/1 "2019-02-22T07:40:27Z")

</div>

I am trying to solve a convex QP. Let us consider the following example:

```julia
using JuMP, CPLEX
m = Model(with_optimizer(CPLEX.Optimizer))
@variable(m,x[1:5],lower_bound=0)
A = rand(5,5).*2 .- 1
c = rand(5,1)
A = A'*A
@objective(m,Min,sum(A[i,j]*x[i]*x[j] for i=1:5, j=1:5)+sum(c[i]*x[i] for i=1:5))
status = optimize!(m)

```

It is showing me the following error:

> The solver does not support an objective function of type MathOptInterface.ScalarQuadraticFunction{Float64}.

As far as my understanding, JuMP and CPLEX support to solve convex QP. Am I missing something here?

I am using Julia 1.1.0 with the following packages:

“Clp” =\> v"0.6.1"  
“Atom” =\> v"0.7.14"  
“CPLEX” =\> v"0.4.3"  
“JuMP” =\> v"0.19.0"  
“Juno” =\> v"0.5.4"  
“Conda” =\> v"1.2.0"  
“ExcelReaders” =\> v"0.10.3"  
“MathProgBase” =\> v"0.7.7"  
“XLSX” =\> v"0.4.6"  
“Cbc” =\> v"0.6.0"  
“DataFrames” =\> v"0.17.1".

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<div class="post-metadata">

**Author:** ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)\
**Post date:** [February 22, 2019, 8:39am UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/2 "2019-02-22T08:39:53Z")

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I don’t know the CPLEX.jl wrapper in detail, but maybe quadratic objectives are not supported directly, but require an auxiliary variable with a bounding constraint. At least that is true for SCIP.jl.

See also the discussion in this issue for a generic solution: [https://github.com/JuliaOpt/MathOptInterface.jl/issues/529](https://github.com/JuliaOpt/MathOptInterface.jl/issues/529)

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<div class="post-metadata">

**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:** [February 22, 2019, 2:32pm UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/3 "2019-02-22T14:32:53Z")

</div>

The CPLEX wrapper hasn’t implemented the quadratic objectives yet. Pull requests accepted 🙂

It shouldn’t be too hard because you can copy the Gurobi implementation (it’s more or less just matching up the different C names).

You would need to edit the [`CPLEX/src/MOI_wrapper.jl`](https://github.com/JuliaOpt/CPLEX.jl/blob/master/src/MOI_wrapper.jl) and add the functions beginning with `LQOI.` and containing `quadratic` in the Gurobi wrapper:  
[https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI\_wrapper.jl#L311-L367](https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI_wrapper.jl#L311-L367)

You also have to add these lines to the list of supported objectives  
[https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI\_wrapper.jl#L9](https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI_wrapper.jl#L9)  
and constraints  
[https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI\_wrapper.jl#L17-L19](https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI_wrapper.jl#L17-L19)

Issue: [https://github.com/JuliaOpt/CPLEX.jl/issues/217](https://github.com/JuliaOpt/CPLEX.jl/issues/217)

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<div class="post-metadata">

**Author:** ![Rajat\_Sanyal](https://avatars.discourse-cdn.com/v4/letter/r/4da419/32.png) [@Rajat\_Sanyal](https://discourse.julialang.org/u/Rajat_Sanyal)\
**Post date:** [March 7, 2019, 1:24pm UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/4 "2019-03-07T13:24:18Z")

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> [@odow](#):
>
> LQOI.get\_number\_quadratic\_constraints

It is giving me the following error:

> delq! not defined

Line 361 in [https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI\_wrapper.jl#L311-L367](https://github.com/JuliaOpt/Gurobi.jl/blob/f1418b5c470fb91b417e3424241a3440078c9212/src/MOI_wrapper.jl#L311-L367)

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<div class="post-metadata">

**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 7, 2019, 2:31pm UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/5 "2019-03-07T14:31:08Z")

</div>

You will need to replace Gurobi-specific functions like `delq!(model.inner)` with the appropriate CPLEX one.

Looking through the [CPLEX API](https://github.com/JuliaOpt/CPLEX.jl/blob/bb3f45c236fb0afb2fa2ed75c448e17b9a64a61e/src/cpx_quad.jl#L4), it seems that the following should be sufficient (I haven’t tested this):

```julia
function LQOI.set_quadratic_objective!(model::Optimizer, I::Vector{Int}, J::Vector{Int}, V::Vector{Float64})
    @assert length(I) == length(J) == length(V)
    scalediagonal!(V, I, J, 0.5)
    CPLEX.add_qpterms!(model.inner, I, J, V)
    scalediagonal!(V, I, J, 2.0)
    return
end

```

You don’t need `delq` or `_require_update`.

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<div class="post-metadata">

**Author:** ![Rajat\_Sanyal](https://avatars.discourse-cdn.com/v4/letter/r/4da419/32.png) [@Rajat\_Sanyal](https://discourse.julialang.org/u/Rajat_Sanyal)\
**Post date:** [March 8, 2019, 4:24am UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/6 "2019-03-08T04:24:59Z")

</div>

> [@odow](#):
>
> function LQOI.set\_quadratic\_objective!(model::Optimizer, I::Vector{Int}, J::Vector{Int}, V::Vector{Float64}) @assert length(I) == length(J) == length(V) scalediagonal!(V, I, J, 0.5) CPLEX.add\_qpterms!(model.inner, I, J, V) scalediagonal!(V, I, J, 2.0) return end

I think it is still broken.

When I am trying to solve the following problem:

> using JuMP, CPLEX  
> function Opti\_model(A,b)  
> m = Model(with\_optimizer(CPLEX.Optimizer))  
> @variable(m,x[1:5],lower\_bound=0,upper\_bound=1)  
> @objective(m,Min,sum(A[i,j]\*x[i]\*x[j] for i=1:5, j=1:5)+sum(c[i]\*x[i] for i=1:5))  
> JuMP.optimize!(m)  
> return (JuMP.value.(x))  
> end  
> B = rand(5,5).\*2 .- 1  
> c = rand(5,1)  
> Primal\_sol = Opti\_model(B’\*B,c)

it is giving me the following error:

> LoadError: MethodError: no method matching solve\_quadratic\_problem!(::CPLEX.Optimizer)  
> Closest candidates are:  
> solve\_quadratic\_problem!(!Matched::LinQuadOptInterface.MockLinQuadOptimizer) at C:\Users\Administrator.julia\packages\LinQuadOptInterface\ZMx9f\src\mockoptimizer.jl:766

Another instance, I am trying to solve which is basically a QIP problem (convex), that is,

> using JuMP, CPLEX  
> function Opti\_model(A,b)  
> m = Model(with\_optimizer(CPLEX.Optimizer))  
> @variable(m,x[1:5],lower\_bound=0,upper\_bound=1)  
> @variable(m,y[1:5],Bin)  
> @objective(m,Min,sum(A[i,j]\*x[i]\*x[j] for i=1:5, j=1:5)+sum(c[i]\*y[i] for i=1:5))  
> JuMP.optimize!(m)  
> return (JuMP.value.(x))  
> end  
> B = rand(5,5).\*2 .- 1  
> c = rand(5,1)  
> Primal\_sol = Opti\_model(B’\*B,c)

it is throwing me the following error message:

> CPLEX.CplexError(5002, “CPLEX Error 5002: %s is not convex.\n”)

I understand that **y** is a binary variable which makes the optimization problem non-convex, but CPLEX (I am using CPLEX 12.8.0) still should solve it. [[CPLEX 12.6.0 Documentation](https://www.ibm.com/support/knowledgecenter/en/SSSA5P_12.7.0/ilog.odms.studio.help/CPLEX/ReleaseNotes/topics/releasenotes126/newNonconvexMIQP.html)]

Any input from you would be very helpful.

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<div class="post-metadata">

**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 8, 2019, 3:20pm UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/8 "2019-03-08T15:20:28Z")

</div>

You will also need to define the `solve_quadratic_problem` function (and possibly some others as well). Do you have the changes somewhere? Please make a pull request to [CPLEX.jl](https://github.com/juliaopt/cplex.jl) and we can point you in the right direction. The [JuMP contributing guide](https://github.com/JuliaOpt/JuMP.jl/blob/master/CONTRIBUTING.md#contribute-code-to-jump) has links to Git tutorials if you aren’t sure how to make a pull request. Otherwise, I might find some time to implement the quadratic interface next week at [JuMP-dev](http://www.juliaopt.org/meetings/santiago2019/).

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<div class="post-metadata">

**Author:** ![Rajat\_Sanyal](https://avatars.discourse-cdn.com/v4/letter/r/4da419/32.png) [@Rajat\_Sanyal](https://discourse.julialang.org/u/Rajat_Sanyal)\
**Post date:** [March 11, 2019, 9:31am UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/9 "2019-03-11T09:31:28Z")

</div>

Thanks. Your help is much appreciated. I am also trying to accustomed myself with Git.

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<div class="post-metadata">

**Author:** ![trigaut](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/trigaut/32/1911_2.png) [@trigaut](https://discourse.julialang.org/u/trigaut)\
**Post date:** [April 10, 2019, 2:19pm UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/10 "2019-04-10T14:19:51Z")

</div>

Hi,

I am trying to add quadratic support to CPLEX.jl with MOI.

I use this test example from matlab doc (the first one with numerical results):  
[[Quadratic programming - MATLAB quadprog - MathWorks France](https://fr.mathworks.com/help/optim/ug/quadprog.html)](qp example)

My test code is the following :

```julia
using JuMP, CPLEX

m = Model(with_optimizer(CPLEX.Optimizer))

@variable(m, x)
@variable(m, y)
@constraint(m, x+y <= 2)
@constraint(m, -x+2*y <= 2)
@constraint(m, 2*x+y <= 3)

@objective(m, Min, 0.5*x*x + y*y - x*y - 2*x - 6*y)

optimize!(m)

value(x), value(y), objective_value(m)

```

And I added the following code as suggested above in MOI\_wrapper.jl of the CPLEX.jl package :

```julia
function LQOI.set_quadratic_objective!(model::Optimizer, I::Vector{Int}, J::Vector{Int}, V::Vector{Float64})
    @assert length(I) == length(J) == length(V)
    #scalediagonal!(V, I, J, 0.5)
    CPLEX.add_qpterms!(model.inner, I, J, V)
    #scalediagonal!(V, I, J, 2.0)
    return
end

LQOI.solve_quadratic_problem!(model::Optimizer) = LQOI.solve_linear_problem!(model)

```

I commented the `scalediagonal!` function @odow as CPLEX kept returning that the matrix Q was not positive semi definite in my test case (which is absurd).

Now CPLEX seems to solve the problem properly. I obtain the same objective value as the matlab page, that is, -8.222 in the CPLEX log.

Now I have to define the `get_quadratic_primal_solution!` in MOI\_wrapper as the call to `optimize!` returns

```julia
ERROR: LoadError: MethodError: no method matching get_quadratic_primal_solution!(::CPLEX.Optimizer, ::Array{Float64,1})

```

after the CPLEX output.

I tried this

```julia
function LQOI.get_quadratic_primal_solution!(model::Optimizer, dest)
    dest = CPLEX.get_solution(model.inner)
    return
end

function LQOI.get_quadratic_dual_solution!(model::Optimizer, dest)
    dest = CPLEX.get_constr_duals(model.inner)
    return
end

```

and the test example runs perfectly.  
BUT the inconsistency with the definitions of `LQOI.get_linear_primal_solution!` `LQOI.get_linear_dual_solution!` is troubling me. I wonder if I miss some MOI feature.  
Could you check my implementation?

Finally everything works fine with small QP and QCP examples from `MOIT.contquadratictest` written with JuMP macros.  
However I added the `MOIT.contquadratictest` tests in the Tests of CPLEX.jl and 6 out of 42 quadratic tests do not pass. Should I do a pull request to get some help?

Thanks

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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:** [April 10, 2019, 4:39pm UTC](https://discourse.julialang.org/t/quadratic-programming-problem-cpl/21068/11 "2019-04-10T16:39:30Z")

</div>

Yes, make a PR.

`get_quadratic_primal_solution` and `get_quadratic_dual_solution` are the solutions associated with the quadratic constraints, not the primal variables.