The reason why variable y always cannot be optimized

1

Hello everyone. The following problem is solved by SCA method. However, the variable y always cannot be optimized. The code is as follows:
G1=[2751500866382.23;446808118241.926;326257521174.188;119205179806.157;165561170834.964;552998169457.887;65920638147.0425;1384098869451.64;70931293899.4374;239837026208.236];
G2=[282941933.951478;282943715.633436;282943973.230548;282934076.208799;282934916.773623;282943536.993081;282945118.896877;282938821.315665;282932539.145752;282935763.819671];
N=10;
vepsilon=500e3ones(N,1);
lambda=2000ones(N,1);
T_off=[5.05858218005831;3.46021631866850;7.45379891387635;1.83424878510173;1.61592161750176;5.98499798271207;5.79409612139907;4.51517450060601;5.08574278575306;7.33088217643273];

F1=32e9;
F2=32e9;
F3=0.5e9;
B=1e6;
para=log(2);
kesai=1;

x1_ba_last=-6*ones(N,1);
x2_ba_last=-4*ones(N,1);
sum_value_last=0;
t=1;
while (kesai>1e-10&&t<10) 
cvx_begin
    variables   x1_ba(N,1) x2_ba(N,1)  p1(N,1) p2(N,1)  tao1_ba(N,1) tao2_ba(N,1) f1_ba(N,1)  f2_ba(N,1);

Status: Solved
Optimal value (cvx_optval): +4.9187
The optimal value of variable p1, p2 is provided as ：
p1=[0.0001;0.00088;0.00083;0.001795;0.001664;0.00043;0.00349;0.000208;0.003435;0.00089];
p2=[0.9941;0.9854;0.9928;0.9981;0.9932;0.9474;0.9954;0.9955;0.9925;0.9956];

However, if we adopt p1=0.5 and p2=0.5, the result is

Status: Solved
Optimal value (cvx_optval): +4.15158
Can you help me to analyze it? Thanks!

2

In general, when you use SCA you’re on your own. It is not guaranteed to converge to anything, let alone a global or even local optimum of the original (non-convex) problem. SCA can converge to a solution which is not a global optimum. It appears that happened to you.

Also, having very large (magnitude) input data is usually not a good thing from the standpoint of reliable algorithm (solver) performance. Nor is very small magnitude (but non-zero) input data.

3

Thank you for your kind reply, Mark. Did you mean the value of G1 and G2 are too large?

4

Yes, among many others. Try to choose units to make numbers closer to 1 in magnitude.

5

Thank you very much, Mark!