# The optimization variables are all large numbers and do not meet the limiting conditions given by me. The optimal solution is positive infinity. Why does this happen?

my code:
function [pBest,numOfLoop,Tafter,Tbefore] = functionPowerOptimization_maxSumRate_refine_1(N,a,b,p,beta,Pmax,tau_p,Tbefore,tau_c)
L= size(beta,1);
%Extract the number of UEs
K = size(beta,2);
dl_power=(K/L)*(Pmax/K)*ones(L,K);
x=zeros(K,1);
Tafter=1e6;
%%%Set the accuracy of the bisection
delta =1e-8;
numOfLoop=0;

while norm((Tafter - Tbefore)/Tbefore) > delta

``````numOfLoop=numOfLoop+1;
if numOfLoop==1

[signal,interf,perUserSE] = functionComputePerUserSE_DL(a,b,K,N,beta,p,tau_p,tau_c,dl_power);
x=signal./(signal+interf);

pBest = functionFeasibilityProblemP1(L,K,N,beta,Pmax,p,a,b,tau_p,x);

Tbefore=sum(perUserSE);
Tafter = functionComputeSumSE_DL(a,b,K,N,beta,p,tau_p,tau_c,pBest);

else
[signal,interf,perUserSE] = functionComputePerUserSE_DL(a,b,K,N,beta,p,tau_p,tau_c,pBest);
x=signal./(signal+interf);

Tbefore=Tafter;
pBest = functionFeasibilityProblemP1(L,K,N,beta,Pmax,p,a,b,tau_p,x);

Tafter = functionComputeSumSE_DL(a,b,K,N,beta,p,tau_p,tau_c,pBest);

end
``````

end
end
function nuSolution = functionFeasibilityProblemP1(L,K,N,beta,Pmax,p,a,b,tau_p,x)
cvx_begin gp
variable nu(L,K); %Power allocation
expression proSINR
% expressions SINR(K,1) numerator(K,1) denominator1(K,1) denominator2(K,1) denominator2s(K,1);
proSINR=1;
for k=1:K
proSINR=proSINR*(NNLL(prod(sqrt(nu(:,k)))prod(a(:,k)))^(2/L)/((Nsum(nu(:,k).a(:,k).beta(:,k)))+(tau_ptau_pNpsum(sum(nu(:,[1:k-1 k+1:end]).*b(:,[1:k-1 k+1:end]).^2.*beta(:,[1:k-1 k+1:end]).repmat(beta(:,k),[1 K-1]))))+(Nsum(sum(nu(:,[1:k-1 k+1:end]).*b(:,[1:k-1 k+1:end]).^2.*repmat(beta(:,k),[1 K-1]))))+1))^x(k)
end
maximize proSINR
subject to
for l = 1:L
% exp(nu(l,:))>=0;
% sum(exp(nu(l,:))) <= (K/L)*Pmax; %%%%% 逐行相加
nu(l,:)>=0;
sum(nu(l,:)) <= (K/L)*Pmax; %%%%% 逐行相加
end

cvx_end

nuSolution = nu;
cvx_optval
end

When I use this function to get the solution of the optimization problem，matlab command window output:

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

proSINR =

``````cvx log-concave expression (scalar)
``````

## Calling Mosek 9.1.9: 12739 variables, 4479 equality constraints For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4479
Cones : 4220
Scalar variables : 12739
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.05
Lin. dep. - number : 0
Presolve terminated. Time: 0.25
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4479
Cones : 4220
Scalar variables : 12739
Matrix variables : 0
Integer variables : 0

Optimizer - solved problem : the primal
Optimizer - Constraints : 4420
Optimizer - Cones : 4220
Optimizer - Scalar variables : 12670 conic : 12660
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.53 dense det. time : 0.05
Factor - ML order time : 0.19 GP order time : 0.00
Factor - nonzeros before factor : 2.12e+04 after factor : 2.86e+04
Factor - dense dim. : 90 flops : 1.14e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.6e+02 2.4e+01 5.4e+04 0.00e+00 5.393775126e+04 0.000000000e+00 1.0e+00 1.33
1 8.8e+01 1.3e+01 3.1e+04 -4.59e-01 4.386239375e+04 2.601048414e+00 5.5e-01 2.03
Optimizer terminated. Time: 2.20

Interior-point solution summary
Problem status : PRIMAL_INFEASIBLE
Solution status : PRIMAL_INFEASIBLE_CER
Dual. obj: 1.7437028082e+00 nrm: 2e+00 Viol. con: 0e+00 var: 6e-01 cones: 0e+00
Optimizer summary
Optimizer - time: 2.20
Interior-point - iterations : 1 time: 2.11
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: Solved
Optimal value (cvx_optval): +Inf

cvx_optval =

Inf

The optimization variables are all large numbers and do not meet the limiting conditions given by me. The optimal solution is positive infinity. Why does this happen?

it appears that your problem is (primal) unbounded (Mosek declares primal infeasible, but it was provided the dual by CVX). I don’t know why CVX Status is Solved rather than Unbounded.

I have limited the value of optimization variables. Why does it lead to boundless problems and cvx_optval =Inf ?