The number scale：
%K=50, B_max=10^7
%a_r(k,m)：binary variable
%L(k)：10^6;
%0<P_L6(k,m)<1
%wew(k,m):10^6;
%f_u:10^9
%0<b(k)<1;
cvx_begin
variables yita B(K);
expression t_ue1(K-N,M)
expression t_ue2(N,M)
minimize(yita);
subject to
for k=N+1:K
for m=1:M
t_ue1(k,m)=a_r(k,m)*(L(k)/P_L6(k,m)*inv_pos(-rel_entr(B(k),B(k)+wew(k,m))/log(2))+L(k)/f_u);
end
end
for k=1:N
for m=1:M
t_ue2(k,m)=b(k)a_r(k,m)(L(k)/P_L6(k,m)*inv_pos(-rel_entr(B(k),B(k)+wew(k,m))/log(2))+L(k)/f_u);
end
end
ee=0;
for k=1:K
ee=ee+B(k);
end
ee<=B_max;
for k=N+1:K
for m=1:M
yita>=t_ue1(k,m);
end
end
for k=1:N
for m=1:M
yita>=t_ue2(k,m);
end
end
cvx_end
Successive approximation method to be employed.
For improved efficiency, SDPT3 is solving the dual problem.
SDPT3 will be called several times to refine the solution.
Original size: 1221 variables, 501 equality constraints
150 exponentials add 1200 variables, 750 equality constraints
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
0/ 40 | 1.419e+00 1.065e+05 1.065e+05 | Failed
0/ 72 | 1.619e-01 4.838e+03 4.838e+03 | Failed
0/ 65 | 5.889e-02 1.615e+04 1.615e+04 | Failed
Status: Failed
Optimal value (cvx_optval): NaN
Calling Mosek 9.1.9: 1221 variables, 501 equality constraints
For improved efficiency, Mosek is solving the dual problem.
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 : 501
Cones : 300
Scalar variables : 1221
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 200
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 501
Cones : 300
Scalar variables : 1221
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 201
Optimizer - Cones : 300
Optimizer - Scalar variables : 902 conic : 900
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 : 1626 after factor : 1676
Factor - dense dim. : 0 flops : 5.30e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.9e+00 5.4e+07 6.0e+08 0.00e+00 6.009481902e+08 0.000000000e+00 1.0e+00 0.05
1 2.5e+00 3.5e+07 4.9e+08 -1.00e+00 6.009480718e+08 -5.342663542e-01 6.5e-01 0.11
2 1.2e+00 1.6e+07 3.3e+08 -1.00e+00 6.009474159e+08 -2.368382534e+00 3.0e-01 0.11
3 3.7e-01 5.2e+06 1.9e+08 -1.00e+00 6.009441205e+08 -9.422354411e+00 9.6e-02 0.11
4 1.4e-01 1.9e+06 1.1e+08 -1.00e+00 6.009356496e+08 -2.681535677e+01 3.6e-02 0.13
5 4.4e-02 6.1e+05 6.4e+07 -1.00e+00 6.009059533e+08 -8.755122480e+01 1.1e-02 0.13
6 4.5e-03 6.2e+04 2.0e+07 -1.00e+00 6.005244967e+08 -8.677163662e+02 1.2e-03 0.13
7 1.4e-05 1.9e+02 1.0e+06 -9.99e-01 4.901738679e+08 -2.272576111e+05 3.6e-06 0.13
8 7.1e-06 9.8e+01 6.0e+05 -6.32e-01 4.135327064e+08 -9.978695379e+05 1.8e-06 0.14
9 4.7e-06 6.4e+01 4.0e+05 -3.71e-01 3.363068532e+08 -1.709920156e+07 1.2e-06 0.14
10 3.0e-07 4.1e+00 2.3e+04 -1.56e-01 3.116798827e+07 -1.711739979e+07 7.6e-08 0.14
11 1.0e-09 1.4e-02 6.1e+00 8.80e-01 7.431403781e+04 -1.036532017e+05 2.6e-10 0.14
12 4.3e-11 6.0e-04 5.2e-02 1.00e+00 3.061816850e+03 -4.371338124e+03 1.1e-11 0.14
13 8.1e-12 1.1e-04 3.8e-03 9.96e-01 7.067847110e+02 -6.802616919e+02 2.0e-12 0.16
14 8.0e-12 1.1e-04 3.7e-03 9.88e-01 7.034460486e+02 -6.763159179e+02 2.0e-12 0.16
15 8.0e-12 1.1e-04 3.7e-03 9.88e-01 7.034460486e+02 -6.763159179e+02 2.0e-12 0.16
16 8.0e-12 1.1e-04 3.7e-03 9.86e-01 7.034460486e+02 -6.763159179e+02 2.0e-12 0.17
Optimizer terminated. Time: 0.20
Interior-point solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 7.0344604861e+02 nrm: 4e+05 Viol. con: 9e-06 var: 0e+00 cones: 4e-17
Dual. obj: -6.7631591791e+02 nrm: 3e+07 Viol. con: 0e+00 var: 1e+02 cones: 0e+00
Optimizer summary
Optimizer - time: 0.20
Interior-point - iterations : 17 time: 0.17
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: Failed
Optimal value (cvx_optval): NaN
The Status of SDPT3 and MOSEK are both Failedu.But when use SDPT3 the solve value of B(k) looks like right and use Mosek the solve value of B(k) is completely wrong.