```
(quad_over_lin(zeta,theta(i))+sum((real(TRC2)+segma))-(inv_pos(sinr(k))*(real(trace(H(:,:,i,i)*H(:,:,i,i)'*W(:,:,i))))))<=0;
```

hence .

TRC2 = TRC2 + trace(H(:,:,j,i)*H(:,:,j,i)β*W(:,:,j));

```
(quad_over_lin(zeta,theta(i))+sum((real(TRC2)+segma))-(inv_pos(sinr(k))*(real(trace(H(:,:,i,i)*H(:,:,i,i)'*W(:,:,i))))))<=0;
```

hence .

TRC2 = TRC2 + trace(H(:,:,j,i)*H(:,:,j,i)β*W(:,:,j));

What specifically is the issue? Are you saying that the constraint is not satisfied? Solvers only have to satisfyconstrains to within a tolerance. For instance, if the LHS of the constraint winds up being 1e-9, that would be considered to satisfy the constraint. If you are not satisfied by this, you can add a small positive number, such as 1e-6, to the LHS in order to ensure that your original constraint is not violated at all.

Also, do the solver and CVX report that the problem is solved to optimality?

Also, if any of zeta, theta, TRC2,sinrr, H, W are CVX expressions (and not CVX variables or MATLAB variables), when you evaluate the constraint after CVX concludes, it may appear that the constraint is not satisfied even if it i. That is because CVX expressions are not guaranteed to have their optimal value, but instead must be recomputed starting from CVX variables. However, the expressions are evaluated correctly during the optimization.

If none of these resolve your difficulty, please post the solver and CVX output, as well as the evidence that the results is βdisappointing in one constraintβ.

1 Like

thank you very much for rapid reply and for your concern and valuable informations

the specifically is the issue is

β**Efficient Energy Transmission on a SWIPT Interference Channel Under**

**Non-linear energy harvesting Models**β

i changed cvx version to 2.2, Build 1148 (62bfcca) and i got no error and the results :

For improved efficiency, SDPT3 is solving the dual problem.

SDPT3 will be called several times to refine the solution.

Original size: 306 variables, 105 equality constraints

3 exponentials add 24 variables, 15 equality constraints

Mov/Act | Centering Exp cone Poly cone | Status

--------Β±--------------------------------Β±--------

0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Infeasible

Status: Unbounded

Optimal value (cvx_optval): +Inf

the cvx part of the code is:

cvx_begin

variables t(1,M) x(1,M) y(1,M) %slack variables.

variable W(N,N,M) complex semidefinite % beamforming or precoding vector.

variable theta(1,M) %power splitting factor 0<theta<1 .

```
maximize (sum(t))
subject to
for i = 1:M
0<=theta(i);
theta(i)<=1;
x(i)>=0;
y(i)>=0;
t(i)>=0;
((di*t(i))+ci)-((mi/(1+x_old(i)))-(mi/square((1+x_old(i))))*(x(i)-x_old(i)))<=0;
(-log(x(i)))-(ai*(2*y_old(i)*y(i)-square(y_old(i))))+(ai*bi)<=0;
(W(:,:,i)) == hermitian_semidefinite(N);
real(trace(W(:,:,i)))-p<=0;
TRC = cvx(0);
TRC2 = cvx(0);
for j = 1:M
TRC = TRC + trace(H(:,:,j,i)*H(:,:,j,i)'*W(:,:,j));
if i~=j
TRC2 = TRC2 + trace(H(:,:,j,i)*H(:,:,j,i)'*W(:,:,j));
end
end
for k=1:lk
th=(1-theta(i));
quad_over_lin(y(i),th)-sum((real(TRC)+segma))<=0;
(mu*inv_pos(th))-sum((real(TRC)+segma))<=0;
(quad_over_lin(zeta,theta(i))+sum((real(TRC2)+segma))-(inv_pos(sinr(k))*(real(trace(H(:,:,i,i)*H(:,:,i,i)'*W(:,:,i))))))<=0;
end
end
cvx_end
x_old = x;
y_old = y;
MHE(1:5) = sum(t); % the maximum harvested energy.
```

![image|488x64](upload://tUEN8YrtytbDBuqO uQBvosomS0n.png)

The solver is solving the dual problem, and reports it is infeasible, so CVX conclude that your original (primal) problem is unbounded. See https://yalmip.github.io/debuggingunbounded/ for tips on diagnosing that.

Given that your model involves log of CVX variable, I recommend that you either use Mosek 9.2 as solver, if that is available to you, oi if not, follow the advice in CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions

1 Like

Thanks a lot for your attention and very fast reply

surely i will apply your valuable advises

best wishes for you

sir i tried mosek as a solver but the results as follow:

CVX Warning:

Models involving βlogβ or other functions in the log, exp, and entropy

family are solved using an experimental successive approximation method.

This method is slower and less reliable than the method CVX employs for

other models. Please see the section of the userβs guide entitled

The successive approximation method

for more details about the approach, and for instructions on how to

suppress this warning message in the future.

For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)

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

Platform: Windows/64-X86

MOSEK warning 62: The A matrix contains a large value of -1.9e+10 in constraint ββ (38) at variable ββ (8).

MOSEK warning 62: The A matrix contains a large value of -1.9e+10 in constraint ββ (42) at variable ββ (8).

MOSEK warning 62: The A matrix contains a large value of 1.8e+10 in constraint ββ (43) at variable ββ (8).

MOSEK warning 62: The A matrix contains a large value of 2.5e+12 in constraint ββ (45) at variable ββ (8).

MOSEK warning 62: The A matrix contains a large value of 1.5e+10 in constraint ββ (46) at variable ββ (8).

MOSEK warning 62: The A matrix contains a large value of 1.4e+16 in constraint ββ (47) at variable ββ (8).

MOSEK warning 62: The A matrix contains a large value of 2.3e+12 in constraint ββ (42) at variable ββ (28).

MOSEK warning 62: The A matrix contains a large value of 1.1e+12 in constraint ββ (44) at variable ββ (28).

MOSEK warning 62: The A matrix contains a large value of 2.5e+16 in constraint ββ (45) at variable ββ (28).

Mosek error: MSK_RES_ERR_HUGE_AIJ (A numerically huge value is specified for an element in A.)

Status: Error

Optimal value (cvx_optval): NaN

Reference to non-existent field βsolβ.

Error in cvx_mosek

Error in cvxprob/solve (line 429)

[ x, status, tprec, iters, y ] = shim.solve( At, b, c, cones, quiet, prec, solv.settings, eargs{:} );

Error in cvx_end (line 88)

solve( prob );

Error in EHEMANS (line 100)

cvx_end

The scaling in your problem is terrible. You need to change units so that non-zero numbers in model coefficients are closer to 1 in magnitude. Mosek (nor any other solver) doesnβt like very large or small magnitude numbers. Fortunately, Mosek warns you about this.

If you for instance have

exp(20*(x+y))

then do not write

exp(20)*exp(x+y)

I know these mathematically is the same, but the first one does not involve insane constants.

@Erling How huge does a number have to be for Mosek to issue

## Mosek error: MSK_RES_ERR_HUGE_AIJ (A numerically huge value is specified for an element in A.)

as opposed to a warning, such as

## MOSEK warning 62: The A matrix contains a large value of 2.5e+16 in constraint ββ (45) at variable ββ (28).

@Mark_L_Stone You can decide! But 1e+20 by default

https://docs.mosek.com/9.2/capi/parameters.html#mosek.dparam.data_tol_aij_huge

@Michal_Adamaszek Thanks. I can tell you that out in the real world, there are many people* who would fix such an error, including on systems involving life or death of large numbers of people, by setting `MSK_DPAR_DATA_TOL_AIJ_HUGE`

to `inf`

. VoilΓ , problem solved, ha ha. (well, it would be funny if large numbers of people might not die as a result).

- And this includes in organizations CMMI level 5 (the highest level) certified in software engineering.

We try help users by warning them about potentially βbadβ things.

You can of course ignore those warnings or turn them off just like you can drive without your seat belt fasten.

1 Like