I built a model to maximize the and sum-rate of the system. The optimization variable is power. Here is my code：
function [feasible,nuSolution] = functionFeasibilityProblemP1(L,K,N,beta,Pmax,gamma,SINRconstraint,P0)
% Pmax = 20;
cvx_begin
variable nu(L,K) %Power allocation
expressions object(K,1) daoshuUI(K,1) daoshuDS(K,1) daoshuRminus(K,1) TaylorDS(K,1) TaylorRminus(K,1)
for k=1:K
daoshuUI(k)=Ksum(beta(:,k));
daoshuDS(k)=Nsqrt(P0(:,k))’*sqrt(gamma(:,k))*sum(sqrt(gamma(:,k))./(sqrt(P0(:,k))+eps));
daoshuRminus(k)=-daoshuUI(k)/((sum(P0’*beta(:,k))+1)*log(2));
TaylorDS(k)=log(sum(nu’beta(:,k))+1+N(sqrt(P0(:,k))’*sqrt(gamma(:,k)))^2+daoshuDS(k)*sum(sum(nu-P0)))/log(2);
TaylorRminus(k)=-log(sum(P0’*beta(:,k))+1)/log(2)+daoshuRminus(k)sum(sum(nu-P0));
object(k)=TaylorDS(k)+TaylorRminus(k);
object(k)>=SINRconstraint;
end
maximize sum(object)
subject to
for l = 1:L
sum(exp(nu(l,:))) <= PmaxK/L; %%%%% 逐行相加
nu(l,:)>=0;
end
cvx_end
% cvx_optval
if contains(cvx_status,‘Solved’) % feasible
feasible = true;
nuSolution = nu;
feasible = false;
nuSolution = [];
end
end
The problem cannot be solved. The solution information is as follows：
CVX Warning:
Models involving “log” 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 user’s 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.
Calling Mosek 9.1.9: 1090 variables, 470 equality constraints
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 : 470
Cones : 220
Scalar variables : 1090
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 : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.02
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 470
Cones : 220
Scalar variables : 1090
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 12
Optimizer - solved problem : the primal
Optimizer - Constraints : 250
Optimizer - Cones : 220
Optimizer - Scalar variables : 890 conic : 660
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 : 1.11e+04 after factor : 1.15e+04
Factor - dense dim. : 0 flops : 9.43e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.6e+02 1.5e+00 2.0e+02 0.00e+00 2.388636706e+01 -1.771224403e+02 1.0e+00 0.05
1 5.5e+01 5.0e-01 5.3e+01 2.74e-01 1.555409766e+02 6.260533816e+01 3.4e-01 0.13
2 1.8e+01 1.6e-01 1.1e+01 5.83e-01 2.147477968e+02 1.791966303e+02 1.1e-01 0.13
3 6.9e+00 6.2e-02 3.1e+00 7.02e-01 2.258734142e+02 2.099128687e+02 4.2e-02 0.13
4 3.4e+00 3.1e-02 1.3e+00 6.85e-01 2.337170816e+02 2.245303460e+02 2.1e-02 0.13
5 8.8e-01 7.9e-03 3.0e-01 4.08e-01 2.393061459e+02 2.353737326e+02 5.4e-03 0.14
6 2.8e-01 2.5e-03 1.6e-01 -7.47e-01 2.504830573e+02 2.465423584e+02 1.7e-03 0.14
7 5.5e-02 5.0e-04 7.7e-02 -8.52e-01 2.645186403e+02 2.610748824e+02 3.4e-04 0.14
8 6.8e-03 6.2e-05 2.6e-02 -9.68e-01 2.556770109e+02 2.608850848e+02 4.2e-05 0.16
9 4.1e-05 3.7e-07 2.0e-03 -9.96e-01 2.569956936e+02 1.830460862e+03 2.5e-07 0.16
10 8.0e-12 7.2e-14 8.8e-07 -1.00e+00 2.588065164e+02 8.207673978e+09 4.9e-14 0.16
Optimizer terminated. Time: 0.20
Interior-point solution summary
Problem status : PRIMAL_INFEASIBLE
Solution status : PRIMAL_INFEASIBLE_CER
Dual. obj: 1.8257079403e-02 nrm: 5e+00 Viol. con: 0e+00 var: 3e-12 cones: 0e+00
Optimizer summary
Optimizer - time: 0.20
Interior-point - iterations : 10 time: 0.16
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
Calling Mosek 9.1.9: 1090 variables, 470 equality constraints
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
*** Error(1400): blc[1] is too large
*** Error(1400): blc[3] is too large
*** Error(1400): blc[5] is too large
*** Error(1400): blc[7] is too large
*** Error(1400): blc[9] is too large
*** Error(1400): blc[11] is too large
*** Error(1400): blc[13] is too large
*** Error(1400): blc[15] is too large
*** Error(1400): blc[17] is too large
*** Error(1400): blc[19] is too large
*** Error(1400): blc[21] is too large
*** Error(1400): blc[23] is too large
*** Error(1400): blc[25] is too large
*** Error(1400): blc[27] is too large
*** Error(1400): blc[29] is too large
*** Error(1400): blc[31] is too large
*** Error(1400): blc[33] is too large
*** Error(1400): blc[35] is too large
*** Error(1400): blc[37] is too large
*** Error(1400): blc[39] is too large
Mosek error: MSK_RES_ERR_INFINITE_BOUND (A numerically huge bound value is specified.)
Status: Error
Optimal value (cvx_optval): NaN