Hello everybody. I’m using cvx MOSEK solver and everything is ok but the solver ignores one of constraints! there is no warning about using successive approximation method or any complexity due to log,exp and … in objective function. this violation is huge in scale of the problem. here is my code:
cvx_begin
cvx_solver MOSEK;
variable x(L*D*N) nonnegative;
variable v(L*D) binary;
variable y(dimm) binary;
minimize(C*x+rho/2*square_pos(norm(AA*x-z-pp+u)));
subject to
-B*x+subplus(B)*b+M*(y-ones(dimm,1))+M*(subplus(H)*v-min(H,0)*v-2)<=zeros(dimm,1);
B*x+subplus(-1*B)*b-M*y+M*(subplus(H)*v-min(H,0)*v-2)<=zeros(dimm,1);
x>=cons;
cvx_end
as you can see, the model has three variables named x,y,v. other notations are all parameters. parameters and variables are defined as vectors.
I appreciate you in advance.
Readers can’t reproduce (independently verify) because we don’t have the input data.
Please show us the solver and CVX output, as well as your evidence of “huge” constraint violation.
this huge violation is due to ignored constraints. The output doesn’t show any error or warning.
output is as below:
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 31
Cones : 2
Scalar variables : 59
Matrix variables : 0
Integer variables : 8
Optimizer started.
Mixed integer optimizer started.
Threads used: 2
Presolve started.
Presolve terminated. Time = 0.00
Presolved problem: 17 variables, 10 constraints, 24 non-zeros
Presolved problem: 0 general integer, 4 binary, 13 continuous
Clique table size: 0
BRANCHES RELAXS ACT_NDS DEPTH BEST_INT_OBJ BEST_RELAX_OBJ REL_GAP(%) TIME
0 1 1 0 NA 3.3366666759e+02 NA 0.0
0 1 1 0 3.3366667593e+02 3.3366666759e+02 2.50e-06 0.0
An optimal solution satisfying the relative gap tolerance of 1.00e-02(%) has been located.
The relative gap is 2.50e-06(%).
Objective of best integer solution : 3.336666759278e+02
Best objective bound : 3.336666675906e+02
Construct solution objective : Not employed
User objective cut value : Not employed
Number of cuts generated : 0
Number of branches : 0
Number of relaxations solved : 1
Number of interior point iterations: 14
Number of simplex iterations : 0
Time spend presolving the root : 0.00
Time spend optimizing the root : 0.05
Mixed integer optimizer terminated. Time: 0.05
Optimizer terminated. Time: 0.06
Integer solution solution summary
Problem status : PRIMAL_FEASIBLE
Solution status : INTEGER_OPTIMAL
Primal. obj: 3.3366667593e+02 nrm: 1e+03 Viol. con: 0e+00 var: 0e+00 cones: 1e-07 itg: 0e+00
Optimizer summary
Optimizer - time: 0.06
Interior-point - iterations : 0 time: 0.00
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 1 time: 0.05
Status: Solved
Optimal value (cvx_optval): +333.667
Forum readers have no idea what the optimal solution (x, v, y) was, and which constraint(s) were violated.
I’m about to decompose a problem and solve it in parallel. so I’ve provided the input data of one of the subproblem to give it a test if you could. here it is:
L=2;
D=2;
N=4;
rho=4;
M=1000;
dimm=4;
C=[1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0];
AA=[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0];
z=[0
0
0
0];
u=[0
0
0
0];
pp=[76
100
78
80];
B=[-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0];
b=[74
75
95
83
87
73
75
99
97
76
95
95
76
100
78
80];
cons=[0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0];
H=[-1 0 1 0
-1 0 0 1
0 -1 1 0
0 -1 0 1];
Here is my solution using Mosek, having optimal objective value = 333.5. All constraints are satisfied.
x
x =
75.750013252633821
99.750013624545701
77.750012795420091
79.750012829531300
0
0
0
0
0
0
0
0
0
0
0
0
v
v =
0
0
0
0
y
y =
0
0
0
0
-Bx+subplus(B)b+M(y-ones(dimm,1))+M(subplus(H)*v-min(H,0)*v-2)
ans =
1.0e+03 *
-2.906999999542786
-2.920999999576898
-2.882999999170875
-2.896999999204986
B*x+subplus(-1*B)*b-M*y+M*(subplus(H)*v-min(H,0)*v-2)
ans =
1.0e+03 *
-1.924000000457214
-1.922000000423103
-1.947000000829126
-1.945000000795014
x-cons
ans =
75.750013252633821
99.750013624545701
77.750012795420091
79.750012829531300
0
0
0
0
0
0
0
0
0
0
0
0
It’s correct, so maybe there is something worng with other parts of my code. Thank you for your time.