The status is failed

1

i use penalty dual decomposition to solve the problem
then when the inner iterations is 8, the outer iterations is 3, the status is failed

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: 162 variables, 75 equality constraints
6 exponentials add 48 variables, 30 equality constraints

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
3/ 3 | 7.183e-01 2.751e+00 0.000e+00 | Solved
3/ 3 | 1.461e-01 2.820e+00s 0.000e+00 | Solved
3/ 3 | 2.147e-02 1.162e+00 0.000e+00 | Solved
3/ 3 | 2.811e-02s 8.764e-01 0.000e+00 | Solved
3/ 3 | 1.340e-02 7.334e-01 0.000e+00 | Solved
3/ 3 | 7.220e-03 9.656e-01s 0.000e+00 | Solved
3/ 3 | 7.625e-02s 6.536e-01 0.000e+00 | Solved
3/ 3 | 1.695e-02 1.037e+00s 0.000e+00 | Solved
3/ 3 | 2.601e-02s 2.912e+00s 0.000e+00 | Solved

Status: Failed
Optimal value (cvx_optval): NaN

how to solve it

2

That is because CVX’s Successive Approximation method for dealing with exponential cone problems is unreliable.

if you have access to Mosek 9.2 use that as the solver. Otherwise, install CVXQUAD and its exponential.m replacement, and follow the instructions at 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

3

i use the mosek 9.1 solver,but it still failed. should I install the mosek 9.2?

4

Mosek 9.2 might be better, but Mosek 9.1 will still trigger native exponential cone usage by CVX.

Please show us all the solver and CVX output I have no idea what “failure” you incurred with Mosek) . It would be good if you can also show us your program.

5

clear all
penalty
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: 156 variables, 75 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 (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 75
Cones : 45
Scalar variables : 156
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 - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 75
Cones : 45
Scalar variables : 156
Matrix variables : 0
Integer variables : 0

Optimizer - threads : 6
Optimizer - solved problem : the primal
Optimizer - Constraints : 27
Optimizer - Cones : 45
Optimizer - Scalar variables : 141 conic : 135
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 : 81 after factor : 93
Factor - dense dim. : 0 flops : 1.15e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 5.0e+04 3.8e+01 0.00e+00 3.696357106e+01 -6.750000000e-03 1.0e+00 0.11
1 2.5e-01 1.3e+04 1.9e+01 -1.00e+00 3.323239878e+01 -7.705222514e-01 2.5e-01 0.23
2 1.0e-01 5.1e+03 1.2e+01 -9.99e-01 2.706639368e+01 -1.161731802e+00 1.0e-01 0.23
3 2.9e-02 1.5e+03 6.5e+00 -9.98e-01 1.078154212e+00 -2.615062983e+00 2.9e-02 0.25
4 3.8e-03 1.9e+02 2.3e+00 -9.91e-01 -2.143145053e+02 -2.574084622e+00 3.8e-03 0.25
5 7.6e-04 3.8e+01 9.1e-01 -9.24e-01 -9.870882180e+02 -9.572115234e+00 7.6e-04 0.25
6 2.5e-04 1.2e+01 2.9e-01 -4.86e-01 -9.767202918e+02 -2.785367058e+01 2.5e-04 0.25
7 1.0e-04 5.1e+00 8.9e-02 1.05e-01 -5.684162507e+02 -4.703232617e+01 1.0e-04 0.27
8 1.8e-05 8.9e-01 5.2e-03 1.03e+00 -1.186743493e+02 -6.103436452e+01 1.8e-05 0.27
9 3.2e-07 1.6e-02 1.0e-05 1.01e+00 -6.343508826e+01 -6.278840127e+01 3.2e-07 0.27
10 7.3e-08 3.6e-03 9.0e-07 1.34e+00 -5.186069098e+01 -5.175829981e+01 7.3e-08 0.28
11 3.7e-08 1.9e-03 3.5e-07 1.17e+00 -4.888778083e+01 -4.882841088e+01 3.7e-08 0.28
12 1.6e-08 8.2e-04 1.1e-07 1.08e+00 -4.752200602e+01 -4.749191368e+01 1.6e-08 0.28
13 2.3e-09 1.2e-04 7.1e-09 1.03e+00 -4.645153414e+01 -4.644540903e+01 2.3e-09 0.30
14 3.2e-10 1.6e-05 3.5e-10 1.02e+00 -4.633777382e+01 -4.633697771e+01 3.2e-10 0.30
15 1.6e-11 7.9e-07 3.4e-12 1.04e+00 -4.632112758e+01 -4.632109605e+01 1.6e-11 0.30
16 3.4e-12 1.7e-07 3.4e-13 1.00e+00 -4.632025923e+01 -4.632025233e+01 3.4e-12 0.31
17 1.2e-12 5.9e-08 7.2e-14 1.00e+00 -4.632009438e+01 -4.632009191e+01 1.2e-12 0.31
18 8.8e-13 5.7e-08 4.6e-14 1.00e+00 -4.632006765e+01 -4.632006580e+01 8.7e-13 0.31
19 4.8e-13 5.0e-08 1.9e-14 1.00e+00 -4.632003089e+01 -4.632002986e+01 4.8e-13 0.33
20 3.6e-13 1.2e-07 1.2e-14 1.00e+00 -4.632001612e+01 -4.632001535e+01 3.7e-13 0.33
21 1.9e-13 1.4e-07 4.8e-15 1.00e+00 -4.631999262e+01 -4.631999220e+01 2.0e-13 0.33
Optimizer terminated. Time: 0.39

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -4.6319992620e+01 nrm: 1e+05 Viol. con: 6e-10 var: 0e+00 cones: 2e-10
Dual. obj: -4.6319992202e+01 nrm: 5e+04 Viol. con: 0e+00 var: 4e-05 cones: 0e+00
Optimizer summary
Optimizer - time: 0.39
Interior-point - iterations : 21 time: 0.34
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): +46.32

Calling Mosek 9.1.9: 162 variables, 75 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 (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 75
Cones : 45
Scalar variables : 162
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 - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 75
Cones : 45
Scalar variables : 162
Matrix variables : 0
Integer variables : 0

Optimizer - threads : 6
Optimizer - solved problem : the primal
Optimizer - Constraints : 27
Optimizer - Cones : 45
Optimizer - Scalar variables : 147 conic : 135
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 : 87 after factor : 96
Factor - dense dim. : 0 flops : 1.21e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 5.0e+04 3.8e+01 0.00e+00 3.698604141e+01 -6.750000000e-03 1.0e+00 0.06
1 2.6e-01 1.3e+04 1.9e+01 -1.00e+00 3.356821380e+01 -5.952268322e-01 2.6e-01 0.17
2 3.9e-02 1.9e+03 7.5e+00 -9.99e-01 1.121397155e+01 -1.086505839e+00 3.9e-02 0.19
3 6.7e-03 3.4e+02 3.1e+00 -9.94e-01 -1.097204913e+02 -1.926397121e+00 6.7e-03 0.19
4 1.1e-03 5.4e+01 1.1e+00 -9.60e-01 -7.594421707e+02 -6.826525307e+00 1.1e-03 0.19
5 3.4e-04 1.7e+01 4.8e-01 -7.06e-01 -1.365814332e+03 -2.072482012e+01 3.4e-04 0.20
6 1.2e-04 5.9e+00 9.2e-02 1.07e-01 -4.595228733e+02 -4.509643181e+01 1.2e-04 0.20
7 1.9e-05 9.4e-01 6.2e-03 6.44e-01 -1.388137304e+02 -6.453606309e+01 1.9e-05 0.20
8 2.6e-06 1.3e-01 2.8e-04 1.14e+00 -7.628006748e+01 -6.827739469e+01 2.6e-06 0.22
9 3.4e-07 1.7e-02 1.1e-05 1.12e+00 -6.537139154e+01 -6.463381650e+01 3.4e-07 0.22
10 9.5e-08 4.8e-03 1.5e-06 1.40e+00 -5.206875523e+01 -5.190408089e+01 9.5e-08 0.23
11 3.7e-08 1.9e-03 3.7e-07 1.19e+00 -4.842582245e+01 -4.835840286e+01 3.7e-08 0.23
12 1.3e-08 6.6e-04 8.0e-08 1.07e+00 -4.733447525e+01 -4.730962482e+01 1.3e-08 0.23
13 3.7e-09 1.8e-04 1.2e-08 1.04e+00 -4.683552276e+01 -4.682841611e+01 3.7e-09 0.23
14 1.0e-09 5.1e-05 1.7e-09 1.01e+00 -4.670476222e+01 -4.670279977e+01 1.0e-09 0.25
15 2.9e-10 1.4e-05 2.6e-10 1.01e+00 -4.666643320e+01 -4.666587417e+01 2.9e-10 0.25
16 6.1e-11 3.0e-06 2.6e-11 9.97e-01 -4.665480773e+01 -4.665468654e+01 6.1e-11 0.27
17 4.0e-11 2.0e-06 1.4e-11 9.21e-01 -4.665350773e+01 -4.665342177e+01 4.0e-11 0.27
18 1.9e-11 9.3e-07 4.7e-12 9.30e-01 -4.665220487e+01 -4.665216192e+01 1.9e-11 0.27
19 1.1e-11 5.4e-07 2.4e-12 7.51e-01 -4.665154595e+01 -4.665151259e+01 1.1e-11 0.28
20 6.6e-12 4.1e-07 1.2e-12 9.85e-01 -4.665115793e+01 -4.665113735e+01 6.8e-12 0.28
21 3.3e-12 2.0e-07 5.6e-13 4.44e-01 -4.665060947e+01 -4.665058950e+01 3.4e-12 0.28
22 1.7e-12 1.0e-07 2.4e-13 4.44e-01 -4.665024992e+01 -4.665023615e+01 1.7e-12 0.30
23 6.9e-13 4.3e-08 1.1e-13 1.14e-02 -4.664962675e+01 -4.664960926e+01 7.0e-13 0.30
24 2.2e-13 1.4e-08 3.4e-14 1.80e-01 -4.664888593e+01 -4.664886957e+01 2.2e-13 0.31
25 7.6e-14 4.7e-09 1.3e-14 -3.05e-02 -4.664803618e+01 -4.664801534e+01 7.8e-14 0.31
26 3.5e-14 2.2e-09 5.8e-15 1.24e-01 -4.664744273e+01 -4.664742361e+01 3.6e-14 0.33
27 1.2e-14 7.2e-10 2.6e-15 -2.60e-01 -4.664604445e+01 -4.664600990e+01 1.2e-14 0.33
28 4.8e-15 3.0e-10 9.2e-16 1.11e-01 -4.664522362e+01 -4.664519874e+01 4.9e-15 0.33
29 1.4e-15 1.3e-10 3.4e-16 -2.17e-01 -4.664322975e+01 -4.664318867e+01 1.5e-15 0.34
30 4.1e-16 4.6e-11 1.2e-16 -1.57e-01 -4.664075373e+01 -4.664069906e+01 4.2e-16 0.34
31 1.3e-16 5.0e-11 3.8e-17 -5.60e-02 -4.663801755e+01 -4.663795546e+01 1.3e-16 0.34
32 4.6e-17 5.8e-11 1.5e-17 -1.10e-01 -4.663507142e+01 -4.663499377e+01 4.7e-17 0.36
33 1.5e-17 5.8e-11 6.0e-18 -1.92e-01 -4.663053475e+01 -4.663042052e+01 1.5e-17 0.36
34 6.8e-18 7.4e-11 2.4e-18 1.51e-01 -4.662788479e+01 -4.662779670e+01 7.0e-18 0.36
35 2.0e-18 1.0e-10 9.5e-19 -2.21e-01 -4.662114879e+01 -4.662100019e+01 2.1e-18 0.38
36 6.2e-19 2.2e-10 3.2e-19 -1.01e-01 -4.661371189e+01 -4.661353914e+01 6.3e-19 0.38
37 2.0e-19 2.1e-10 1.2e-19 -4.84e-02 -4.660527423e+01 -4.660507844e+01 2.0e-19 0.38
38 6.7e-20 3.1e-10 4.5e-20 -9.20e-02 -4.659564608e+01 -4.659540448e+01 6.8e-20 0.39
39 3.3e-19 2.7e-10 1.6e-20 -1.18e-01 -4.658135224e+01 -4.658102953e+01 1.9e-20 0.39
40 3.6e-19 1.7e-09 7.1e-21 1.56e-01 -4.657346694e+01 -4.657320277e+01 8.6e-21 0.39
41 6.4e-19 1.1e-09 3.3e-21 -1.58e-01 -4.655404182e+01 -4.655365744e+01 4.3e-21 0.41
42 4.4e-19 1.2e-09 8.9e-22 2.45e-01 -4.653985099e+01 -4.653956674e+01 2.0e-21 0.41
43 3.8e-19 1.1e-09 4.7e-22 2.17e-01 -4.651915638e+01 -4.651891098e+01 7.0e-22 0.41
44 2.8e-19 1.4e-09 6.0e-22 1.03e-01 -4.650297781e+01 -4.650270202e+01 4.4e-22 0.42
45 1.6e-19 2.6e-09 3.8e-22 1.96e-01 -4.648640798e+01 -4.648615327e+01 2.3e-22 0.42
46 1.1e-19 2.7e-09 3.3e-22 3.19e-01 -4.647541613e+01 -4.647519394e+01 1.4e-22 0.42
47 7.1e-20 2.9e-09 1.5e-22 2.51e-01 -4.646069046e+01 -4.646047225e+01 8.1e-23 0.44
48 5.0e-20 3.3e-09 3.9e-23 3.98e-01 -4.645056177e+01 -4.645038131e+01 4.6e-23 0.44
49 4.6e-20 2.9e-09 7.1e-23 3.87e-01 -4.644504058e+01 -4.644487157e+01 3.5e-23 0.44
50 4.3e-20 3.8e-09 7.4e-23 3.74e-01 -4.644291187e+01 -4.644274716e+01 3.2e-23 0.45
51 3.1e-20 4.7e-09 7.4e-23 3.59e-01 -4.643101232e+01 -4.643086290e+01 1.6e-23 0.45
52 3.0e-20 6.2e-09 4.4e-23 3.02e-01 -4.642958061e+01 -4.642943519e+01 1.5e-23 0.45
53 3.0e-20 7.2e-09 5.2e-23 3.42e-01 -4.642890910e+01 -4.642876538e+01 1.4e-23 0.47
54 2.7e-20 6.5e-09 3.9e-23 3.37e-01 -4.642531990e+01 -4.642518286e+01 1.2e-23 0.47
55 1.4e-20 8.1e-09 1.7e-23 2.82e-01 -4.641053621e+01 -4.641040592e+01 4.7e-24 0.47
Optimizer terminated. Time: 0.55

Interior-point solution summary
Problem status : ILL_POSED
Solution status : PRIMAL_ILLPOSED_CER
Dual. obj: -5.9690877497e-09 nrm: 5e+02 Viol. con: 0e+00 var: 3e-08 cones: 0e+00
Optimizer summary
Optimizer - time: 0.55
Interior-point - iterations : 55 time: 0.48
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

6

Are you running CVX inside a for loop, where the results from one CVX invocation are fed in as iinputs to the next CVX invocation?

The first Mosek output shows the problem was solved. I suppose the input data was different for the 2nd problem?

Can you show your complete program (preferably with input data)? If you wait a day or so, a Mosek person might be able to provide more specific guidance, if they see your program.

7

thans a lot. this is my complete program:

%%penalty
%parameters
L = 0.5*10^5; %计算比特
T = 0.1; %时间
alpha = 4; %路径损失系数
B = 10^6; %带宽
K = 3; %用户数
epsilon = 0.1; %保密中断概率
c = 10^3; %CPU 转数
zeta = 10^-28; %能量效益系数
sigma = -60;
gamma = [3,2,1];
d = 100;

Nmax = 1000; %内层循环
Rmax = 3000; %外层循环

%for i = 1:length(L)
%feasible point
l1 = [210^4,210^4,210^4];
Rs_old = [0.3,0.3,0.3];
Rt = [0.4,0.4,0.4];
b_old = [0.33,0.33,0.33];
B_old = [0,1,1;0,0,1;0,0,0];
B1 = [0,1,1;0,0,1;0,0,0];
p_old = [0.22,0.25,0.38];
pai_old = [1.9,1.4,1.1];
u_old = [2.4,1.8,1.4];
w_old = [0.54,0.5,0.55];
phi_old = [1.510^-8,1.510^-8,1.510^-8];
sum_energy_old = 0.08524;

tolerance1 = 1e-2;
tolerance2 = 1e-3;

n = 0;
r = 1;

%选取乘子向量的初始值
rou = 10^3;
lam = 0.1*ones(3,K,K);
s = 0.2; %罚因子

%检验中止条件的值
error1 = 10;
error2 = 10;

%外层循环
while(error1>tolerance1 && r<Rmax)
    %内层循环
    while(error2>tolerance2 && n<Nmax)
        lam1 = reshape(lam(1,:,:),K,K);
        lam2 = reshape(lam(2,:,:),K,K);
        lam3 = reshape(lam(3,:,:),K,K);
        B1 =(B_old+ B_old.^2+rou.*lam1+rou*lam2.*B_old)./(1+B_old.^2);
        
        cvx_begin
        cvx_solver mosek
         variable l1(1,K)
         variable p(1,K)
         variable Rt(1,K)
         variable Rs(1,K)  
         variable phi(1,K)
         variable u(1,K) 
         variable pai(1,K)  
         variable w(1,K)
         variable B(K,K)
         variable b(1,K)
         expression m(1,K)
         expression  c1(1,K)
         
        %objective function 
        E = zeta*pow_abs(c,3)*pow_abs(l1,3)./0.01 + p.*T;
        a1 = sum(sum((B-B1+rou.* lam1).^2));
        a2 = sum(sum((B.*(1-B1)+rou.* lam2).^2));
        a3 = sum(sum((B+B'- ones(K) + eye(K) +rou.* lam3).^2));
        fun = sum(E) + 0.5*(1/rou)*(a1 + a2 + a3);
        minimize (fun) 
        
        subject to
        for k = 1:K
           (L - l1(k))-10^5* Rs(k)<=0; 
           Rt(k) - log(1+b(k))<=0;
          for l = 1:K
              m(l) = (B_old(k,l)-gamma(l).*p_old(l))*(B(k,l)-gamma(l).*p(l))*0.25-square(B_old(k,l)-gamma(l).*p_old(l))*0.125;
              c1(l) = B(k,l)+p(l); 
              if  B_old(k,l)~=0  
                 gamma(l)*(B_old(k,l)*p_old(l) + p_old(l)*(B(k,l)-B_old(k,l))+B_old(k,l)*(p(l)-p_old(l)))<=gamma(k).* p(k); 
              end
          end
          c1(k) = [];
          m(k) = [];
          e = [sum(m)+(pai(k)-1)*0.5-0.5,c1(1)*0.5,c1(2)*0.5]; 
           norm(e)<=(pai(k)-1)*0.5+0.5+sum(m);              
           b_old(k)*pai_old(k) + pai_old(k)*(b(k)-b_old(k))+b_old(k)*(pai(k)-pai_old(k))- gamma(k)*p(k)<=0;
           exp(-phi(k)*pow_abs(d,alpha)) <= epsilon;
           pai_old(k)*2^Rs_old(k)+2^Rs_old(k)*(pai(k)-pai_old(k))+pai_old(k)*2^Rs_old(k)*log(2)*(2^Rs(k)-2^Rs_old(k))-u(k)<=0;
           p_old(k)*u_old(k) + u_old(k)*(p(k)-p_old(k))+p_old(k)*(u(k)-u_old(k))- w(k)==0;
           phi_old(k)*w_old(k) + w_old(k)*(phi(k)-phi_old(k))+phi_old(k)*(w(k)-w_old(k))- (pai(k)+gamma(k)*p(k)-u(k))*10^-6<=0; 
        end 
        cvx_end
       %更新各种变量
       error2=abs(fun-sum_energy_old)/abs(sum_energy_old);         
       Rs_old = Rs;
       p_old = p;
       pai_old = pai;
       b_old = b;
       u_old = u;
       w_old = w;
       phi_old = phi;
       B_old = B;
       sum_energy_old= fun;
       n = n+1; 
    end
    error1 = norm([B-B1;B.*(1-B1);B + B'- ones(K) + eye(K)],inf);     
    %更新乘子向量
    if error1<pow_abs(0.3,r)
       lam = lam +  1/rou*error1;
    else
       rou = rou*s;
    end
    r = r+1;
    error2 = 10;
end
8

You need to improve the scaling (choice of units) of your problem. Numbers such as zeta = 10^-28 are generally not good for solvers. Try to get your numbers to be closer to one in magnitude.

I haven’t put in the effort to figure out what you are trying to do with your overall loop. perhaps it diverges, rather than converges to what you want? In any event, starting with huge or tiny input values is not likely a recipe for success.

9

i want minimize the energy consumption for NOMA enabled MEC system。B（k,l) denotes the decoding order. the energy consumption composes two parts: the local and the offloading. i use penalty dual decompsition method.
this is the algorithm.

  1. Define the tolerance of accuracy error1 and error2. Initialize the algorithm with a feasible point. Set the iteration number r=0,i=0. Set s<0 and p>0.
  2. Repeat
    Repeat
    Update B1
    Solve the problem and update the rest of variables
    Update the iteration number r=r+1
    Until meet the tolerance of accuracy error1 or the maximum number of iterations is reached.
    Update the penalty parameter p and dual variable lamda
    Update the Update the iteration number i=i+1
  3. until meet the tolerance of accuracy error2
10

You need much better scaling.