Quadratic objective function

[DiegoLucadeTena]

Is there a way that the Xpress.jl wrapper would anytime accept quadratic objective functions using "mmquad"?

Thank you!

[odow]

What is mmquad?

[odow]

Is this the same issue as #274?

[joaquimg]

Can you expand on what you need?
Mmquad is a mosel library (part of a modeling language) not part of the optimizer.

[odow]

Xpress supports quadratic objective functions. Here's the example from https://www.fico.com/fico-xpress-optimization/docs/latest/mosel/mosel_lang/dhtml/mmquad_secmmquadnf.html

julia> import Xpress_jll

julia> ENV["XPRESS_JL_LIBRARY"] = Xpress_jll.libxprs
"/Users/odow/.julia/artifacts/f74d46af4235b72fa5c28522935999d846c6f11a/lib/libxprs.dylib"

julia> ENV["XPAUTH_PATH"] = "/Users/odow/git/jump-dev/Xpress/xpauth.xpr"
"/Users/odow/git/jump-dev/Xpress/xpauth.xpr"

julia> using JuMP, Xpress

julia> model = Model(Xpress.Optimizer)
A JuMP Model
├ solver: Xpress
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> set_silent(model)

julia> @variable(model, x[1:4])
4-element Vector{VariableRef}:
 x[1]
 x[2]
 x[3]
 x[4]

julia> set_lower_bound(x[1], 2)

julia> set_upper_bound(x[1], 20)

julia> set_integer.(x[2:3])
2-element Vector{Nothing}:
 nothing
 nothing

julia> @constraints(model, begin
           x[1] + 2*x[2] - 4*x[4] >= 0
           3*x[1] - 2*x[3] - x[4] <= 100
           x[1] + 3*x[2] + 3*x[3] - 2*x[4] >= 10
           x[1] + 3*x[2] + 3*x[3] - 2*x[4] <= 30
       end)
(x[1] + 2 x[2] - 4 x[4] ≥ 0, 3 x[1] - 2 x[3] - x[4] ≤ 100, x[1] + 3 x[2] + 3 x[3] - 2 x[4] ≥ 10, x[1] + 3 x[2] + 3 x[3] - 2 x[4] ≤ 30)

julia> @objective(model, Min, x[1] + x[1]^2 + 2*x[1]*x[2] + 2*x[2]^2 + x[4]^2)
x[1]² + 2 x[1]*x[2] + 2 x[2]² + x[4]² + x[1]

julia> optimize!(model)

julia> solution_summary(model)
solution_summary(; result = 1, verbose = false)
├ solver_name          : Xpress
├ Termination
│ ├ termination_status : OPTIMAL
│ ├ result_count       : 1
│ ├ raw_status         : 6 Global search complete - integer solution found ( XPRS_MIP_OPTIMAL). - no interruption - the solve completed normally
│ └ objective_bound    : 4.00000e+00
├ Solution (result = 1)
│ ├ primal_status        : FEASIBLE_POINT
│ ├ dual_status          : NO_SOLUTION
│ ├ objective_value      : 4.00000e+00
│ ├ dual_objective_value : 4.00000e+00
│ └ relative_gap         : 0.00000e+00
└ Work counters
  └ solve_time (sec)   : 2.38013e-03

So I think I'm going to tentatively close this issue as "already fixed." There's no need for mmquad.

If you have a reproducible example of something that isn't working, please comment below and I can re-open the issue.

[DiegoLucadeTena]

Hello!!

Thank you for reaching out, I have conducted further exploration and it seems it is not that is not covered as I thought but that the objective function needs to be provided in a specific way.

Let me provide two pieces of code that illustrate this.

D

This does not work, while I assumed it its because it is not contemplated it seems that the implementation has issues:

    using JuMP
    using Xpress
    
    ucf = Model(Xpress.Optimizer)
    
    @variable( ucf , X  ) ; # Flow
    @variable( ucf , Y  ) ; # Lambda from dual variables
    @variable( ucf , Z  ) ; # Reference flow of previous iteration
    @variable( ucf , FO ) ; # Reference flow of previous iteration
    
    @constraint(ucf, X + Z >= -1000 )
    @constraint(ucf, X + Z <= +1000 )             
    
    @constraint(ucf, FO ==  X * Y  ) ; # + ( X - A )^2
    
    @objective(ucf, Max, FO )          
    
    optimize!(ucf)
    
    fix( ucf[:Y],   20  ;  force = true ) ;
    fix( ucf[:Z],   500 ;  force = true ) ;
    
    optimize!(ucf)

Returning:

FICO Xpress v9.4.0, Hyper, solve started 11:52:32, Sep 8, 2025
Heap usage: 131KB (peak 148KB, 1806KB system)
Maximizing QCQP using up to 8 threads and up to 31GB memory, with these control settings:
OUTPUTLOG = 1
MPSNAMELENGTH = 64
CALLBACKFROMMASTERTHREAD = 1
Original problem has:
4 rows 4 cols 6 elements
2 qrows 2 qrowelem
?900 Warning: The quadratic part of row 'R3' defines a nonconvex region.
Please check your model or use nlpoptimize.
Presolve finished in 0 seconds
Heap usage: 131KB (peak 151KB, 1806KB system)

However this does indeed work:

    using JuMP
    using Xpress
    
    ucf = Model(Xpress.Optimizer)
    
    @variable( ucf , X  ) ; # Flow
    @variable( ucf , Y  ) ; # Lambda from dual variables
    @variable( ucf , Z  ) ; # Reference flow of previous iteration
    # @variable( ucf , FO ) ; # Reference flow of previous iteration
    
    @constraint(ucf, X + Z >= -1000 )
    @constraint(ucf, X + Z <= +1000 )             
    
    # @constraint(ucf, FO ==  X * Y  ) ; # + ( X - A )^2
    
    @objective(ucf, Max, X * Y )          
    
    optimize!(ucf)
    
    fix( ucf[:Y],   20  ;  force = true ) ;
    fix( ucf[:Z],   500 ;  force = true ) ;
    
    optimize!(ucf)

Returning:

FICO Xpress v9.4.0, Hyper, solve started 11:51:28, Sep 8, 2025
Heap usage: 2399KB (peak 2417KB, 1681KB system)
Maximizing QP using up to 8 threads and up to 31GB memory, with these control settings:
OUTPUTLOG = 1
MPSNAMELENGTH = 64
CALLBACKFROMMASTERTHREAD = 1
Original problem has:
2 rows 3 cols 4 elements
2 qobjelem
Presolved problem has:
0 rows 0 cols 0 elements
Presolve finished in 0 seconds
Heap usage: 2398KB (peak 2417KB, 1681KB system)

Its Obj Value S Ninf Nneg Sum Dual Inf Time
0 5400.000000 D 0 0 .000000 0
Uncrunching matrix
Optimal solution found
Dual solved problem
0 simplex iterations in 0.00 seconds at time 0

Final objective : 5.400000000000000e+03
Max primal violation (abs/rel) : 0.0 / 0.0
Max dual violation (abs/rel) : 0.0 / 0.0
Max complementarity viol. (abs/rel) : 0.0 / 0.0

[odow]

Your issue is that you are adding a new decision variable and a non-convex quadratic constraint.

You can do instead:

@expression(ucf, FO, X * Y)
@objective(ucf, Max, FO)

This will make FO an expression that you can use in other parts of the model.

[DiegoLucadeTena]

There is still something that does not work, and the Xpress code above returns an optimal result. Why should this be unbounded?

using JuMP
using Xpress
ucf = Model(Xpress.Optimizer)
@variable( ucf , X  ) ; 
@variable( ucf , Y  ) ; 
@variable( ucf , FO >= 0) ;
@constraint(ucf, X >= -1000 ) ;
@constraint(ucf, X <= +1000 ) ;
@expression(ucf, FO ==  X * Y ) ;
@objective(ucf, Max, FO ) ;
optimize!(ucf) ;
fix( ucf[:Y],   20  ;  force = true ) ;
optimize!(ucf)
fix( ucf[:Y],   20  ;  force = true ) ;
optimize!(ucf)

julia> optimize!(ucf)
FICO Xpress v9.4.0, Hyper, solve started 11:00:07, Sep 9, 2025
Heap usage: 130KB (peak 148KB, 394KB system)
Maximizing LP  using up to 8 threads and up to 31GB memory, with these control settings:
OUTPUTLOG = 1
MPSNAMELENGTH = 64
CALLBACKFROMMASTERTHREAD = 1
Original problem has:
         2 rows            3 cols            2 elements
The problem is unbounded due to column C3
Presolve finished in 0 seconds
Heap usage: 130KB (peak 148KB, 394KB system)

[odow]

Your code isn't doing what you think it is doing.

This line is wrong:

@expression(ucf, FO ==  X * Y ) ;

You needed:

ucf = Model(Xpress.Optimizer)
@variable(ucf , X)
@variable(ucf , Y)
@expression(ucf, FO, X * Y ) ;
@objective(ucf, Max, FO ) ;

Note that FO is NOT a decision variable.

p.s., once you fix that, you'll run into the non-convex issue #274