MOSEK: Problem becomes infeasible when I change the objective function

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cnbrksnr
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MOSEK: Problem becomes infeasible when I change the objective function

Post by cnbrksnr » 1 week ago

Hello all,

I have a moderate-sized LP with ~13k variables and ~25k constraints. When I try to solve using MOSEK, it says that the problem is primal infeasible. By construction, I know a feasible solution exists. Also, when I set the objective function to a constant and then solve the problem, it turns out to be optimal. Furthermore, both problems seems to be optimal when I use KNITRO.
How and why it is happening? Any help would be greatly appreciated.

Below is the code and attached
divided.gdx
(1.03 MiB) Downloaded 15 times
is the GDX file. "model sigma" is infeasible and "model dummy_problem" is optimal.

Code: Select all

$gdxin divided.gdx

Sets
n1
n2
m2
m3
m_ineq
m_eq
m_coupeq
;

$load    n1 n2 m2 m3 m_ineq m_eq m_coupeq

Parameters
c1_sigma(n1)
f1_sigma(n2)
c1_sch(n1)
f1_sch(n2)
Aineq(m_ineq,n1)
bineq1(m_ineq)
Aeq(m_eq,n1)
beq1(m_eq)
Acoupeq(m_coupeq, n1)
Bcoupeq(m_coupeq,n2)
bcoupeq1(m_coupeq)
C(m2,n2)
d1(m2)
F(m3,n2)
g1(m3)
a_i
d_i
x_feas(n1)
y_feas(n2)

$load c1_sigma f1_sigma c1_sch f1_sch C d1 F g1 a_i d_i Aineq bineq1 Aeq beq1 Acoupeq Bcoupeq bcoupeq1 x_feas y_feas
;

Variables
obj_sigma
x(n1)
;


Positive Variable
y(n2)
;

y.fx(n2)$(n2.pos<= a_i)  = 0;
y.fx(n2)$(n2.pos > d_i and n2.pos <= 96)  = 0;
y.fx(n2)$(n2.pos > 96 and n2.pos <= 96 + a_i)  = d1('96');


Equations
const1_eq(m_eq)
const1_ineq(m_ineq)
const1_coupeq(m_coupeq)
const2(m2)
const3(m3)
objeq_sigma
objeq_dummy
;

obj_sigma.up = 0;
obj_sigma.lo = -1;

const1_eq(m_eq).. sum(n1, Aeq(m_eq,n1)*x(n1)) =e= beq1(m_eq);
const1_ineq(m_ineq) .. sum(n1, Aineq(m_ineq,n1)*x(n1)) =g= bineq1(m_ineq);
const1_coupeq(m_coupeq) .. sum(n1, Acoupeq(m_coupeq,n1)*x(n1)) + sum(n2, Bcoupeq(m_coupeq,n2)*y(n2)) =e= bcoupeq1(m_coupeq);
const2(m2).. sum(n2, C(m2,n2)*y(n2)) =e= d1(m2);
const3(m3).. sum(n2, F(m3,n2)*y(n2)) =g= g1(m3);
objeq_sigma.. obj_sigma =e= sum(n1, c1_sigma(n1)*x(n1)) + sum(n2, f1_sigma(n2)*y(n2));
objeq_dummy.. obj_sigma =e= -0.5;


option lp=mosek;

Model dummy_problem / const1_eq, const1_ineq, const1_coupeq, const2, const3, objeq_dummy /;

Model sigma / const1_eq, const1_ineq, const1_coupeq, const2, const3, objeq_sigma /;

sigma.OptFile = 1;
dummy_problem.OptFile = 1;

*Solve dummy_problem using lp minimizing obj_sigma ;
Solve sigma using lp minimizing obj_sigma ;


*display sigma.modelstat;

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dirkse
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Re: MOSEK: Problem becomes infeasible when I change the objective function

Post by dirkse » 1 week ago

Hello,

When I solve your models - using MOSEK with GAMS 36.1.0 on my Linux machine - I get an optimal solution for each one.

I notice you set bounds on the variable obj_sigma. This is almost surely going to be counterproductive. It is common - and justifiable - to conflate the objective variable specified in the solve statement and the objective function of the LP, but only when the obj var is free. If the obj var is bounded, the solver won't treat the obj var specially, and will just use the obj function
1 * obj_sigma (in your case)

HTH,

-Steve

cnbrksnr
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Re: MOSEK: Problem becomes infeasible when I change the objective function

Post by cnbrksnr » 1 week ago

Hello Steve,

Thanks for your reply. I didn't know bounding the objective leads to adverse effects. I am using GAMS 28 due to my licence, on a Windows. The solution returns infeasible for me. Could this be a bug? If so, how can I rectify the issue?

Cheers

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dirkse
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Location: Fairfax, VA

Re: MOSEK: Problem becomes infeasible when I change the objective function

Post by dirkse » 1 week ago

Hello,

If you suspect that there is a bug in GAMS you should contact GAMS support with a minimal reproducible example. Be clear about what you consider wrong, and what you expect instead, and how to reproduce the wrong behavior. Send .log and .lst files illustrating the wrong behavior.

-Steve

cnbrksnr
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Re: MOSEK: Problem becomes infeasible when I change the objective function

Post by cnbrksnr » 1 week ago

Hello Steve,


I had turned off the pre-solver. I turned it on now, and the result returned optimal. I think I am all good.

Thanks for the tips.

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