Mismatch in the cost function in MOSEK with Convex.jl

Specific Domains Optimization (Mathematical)
1

I am using Convex.jl and MOSEK to solve a mixed integer second-order cone programming problem.
The cost function is encoded as
minimize(-x + μ * sum(abs.(v)) - a * sum(γ))
where x (real value), v (real vector), and γ (binary vector) are the problem variables, and a and μ are parameters. I noticed that for high values of μ there is a mismatch between the log of MOSEK and the cost function computed using the results of the variables. Specifically, MOSEK log reports
Objective of best integer solution : -1.342072779625e+01
Best objective bound : -1.342072779625e+01
while if I try to compute the cost function using the results its value is -6.28. Additionally, a cost function having a value lower than -7.21 should be impossible due to the bounds on x and γ.
Is there any explanation for this?

PS: the original problem is quite complex and long. I am trying to find a MWE.

2

Some questions to help debug:

  • Do you have the solution log? What is the status? Did Mosek terminate normally?
  • What are the bounds on x and γ? Did you verify that the solution to x and γ are actually feasible in their bounds?
  • What is a “large” μ?
3

I’ll reply point by point:

  • Yes, it terminates normally, the log is
An optimal solution satisfying the relative gap tolerance of 1.00e+00(%) has been located.
The relative gap is 0.00e+00(%).
An optimal solution satisfying the absolute gap tolerance of 0.00e+00 has been located.
The absolute gap is 0.00e+00.

Objective of best integer solution : -1.342072779625e+01     
Best objective bound               : -1.342072779625e+01
Initial feasible solution objective: Undefined
Construct solution objective       : Not employed
User objective cut value           : Not employed
Number of cuts generated           : 0
Number of branches                 : 611
Number of relaxations solved       : 615
Number of interior point iterations: 18831
Number of simplex iterations       : 0
Time spend presolving the root     : 0.20
Time spend optimizing the root     : 0.30
Mixed integer optimizer terminated. Time: 66.23
  • x must be lower than log(500)=6.21, while the term a * sum(γ) is at maximum 1, since the parameter a is selected to be 1/length(γ). And yes, the solution is feasible, and the bounds and constraints are well respected.
  • Higher than 10000. And it gets worse incresing the value.
4

the solution is feasible, and the bounds and constraints are well respected.

To clarify: you have checked the value of x.value, v.value and γ.value, and these are okay. But problem.optval gives the wrong answer?

Do you have a reproducible example? It’s hard to identify what is going on without one.

5

Exactly, x.value, v.value, and γ.value are okay, but problem.optval gives the wrong answer.

I’ll try to get a MWE and get back here