Hello,

I am new to CVX, and currently trying a small example on cvx to see how it works, (the solver I use is Mosek).

The model I set is to minimize the sum of separable quadratic functions, and the constraints set values to all decision variables x(i) for i = 1,…, 22. Intuitively, this model must be feasible, and gives me the objective value by plugging in x values. However, cvx said this model is infeasible with obj = infinity. I do not understand why this happened. Can anyone help me with this?

I also tried the following things:

- I changed the expression of the objective function to matrix-vector form, but it is still infeasible.
- I changed the objective function to sum of separable linear function with the same constraints, it returns me the correct objective value.
- I used the same separable quadratic objective function, but set constraints as for i = 1:num_arc x(i)==1 end., then it gives me the same objective value.

I got very confused of this. Thank you so much for any help and explanation.

n = 8;

num_arc = 22;

ai = [1, 6, 2, 10, 7, 8, 4, 10, 10, 10, 7, 5, 3, 10, 9, 10, 3, 4, 0, 6, 9, 10];

bivalue = [-8, -5, -3, -7, -1, -6, -7, -9, -6, -8, -5, -7, -10, -10, -9, -3, -8, -8, 0, 0, -4, -9]

ci = [5, 1, 8, 5, 1, 9, 9, 6, 4, 8, 1, 8, 4, 5, 8, 8, 5, 9, 10000, 7, 8, 10]

cvx_begin

variable x(num_arc)

```
obj = 0
for i = 1:num_arc
obj = obj + ai(i)*x(i)^2+bivalue(i)*x(i) + ci(i)
end
minimize(obj)
subject to
x(1) == 29292
x(2) == 57139
x(3) == 0
x(4) == 0
x(5) == 0
x(6) == 0
x(7) == 13569
x(8) == 0
x(9) == 0
x(10) == 29292
x(11) == 0
x(12) == 0
x(13) == 57139
x(14) == 0
x(15) == 0
x(16) == 0
x(17) == 0
x(18) == 0
x(19) == 70708
x(20) == 0
x(21) == 13569
x(22) == 0
```

cvx_end

## log

Calling Mosek 9.1.9: 66 variables, 22 equality constraints

For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)

Copyright © MOSEK ApS, Denmark. WWW: mosek.com

Platform: MACOSX/64-X86

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 22

Cones : 22

Scalar variables : 66

Matrix variables : 0

Integer variables : 0

Optimizer started.

Presolve started.

Eliminator started.

Freed constraints in eliminator : 0

Eliminator terminated.

Eliminator - tries : 1 time : 0.00

Lin. dep. - tries : 0 time : 0.00

Lin. dep. - number : 0

Presolve terminated. Time: 0.03

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 22

Cones : 22

Scalar variables : 66

Matrix variables : 0

Integer variables : 0

Optimizer - threads : 8

Optimizer - solved problem : the primal

Optimizer - Constraints : 0

Optimizer - Cones : 7

Optimizer - Scalar variables : 21 conic : 21

Optimizer - Semi-definite variables: 0 scalarized : 0

Factor - setup time : 0.00 dense det. time : 0.00

Factor - ML order time : 0.00 GP order time : 0.00

Factor - nonzeros before factor : 0 after factor : 0

Factor - dense dim. : 0 flops : 0.00e+00

ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME

0 6.4e+00 1.4e+05 2.4e+01 0.00e+00 7.000000000e+00 -1.650000000e+01 1.0e+00 0.06

1 6.0e-09 6.4e-05 1.7e-06 -1.00e+00 -1.750000161e+01 -1.649999995e+01 4.0e-09 0.32

Optimizer terminated. Time: 0.43

Interior-point solution summary

Problem status : DUAL_INFEASIBLE

Solution status : DUAL_INFEASIBLE_CER

Primal. obj: -1.7500001606e+01 nrm: 7e-01 Viol. con: 0e+00 var: 0e+00 cones: 3e-09

Optimizer summary

Optimizer - time: 0.43

Interior-point - iterations : 1 time: 0.32

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: 0 time: 0.00

Status: Infeasible

Optimal value (cvx_optval): +Inf