When I find the minimum value, the output target value is gradually reduced in the previous iteration, but when the value is about to converge, the value begins to fluctuate ( small range ), resulting in poor convergence effect. What is the reason How should I solve it The numerical fluctuation is shown in the figure.
We have no idea what you did. Did you use some kind of Successive Convex Approximation, and these are the optimal objective values of the iterations?
In general, (unsafeguarded) Successive Convex Approximation is not guaranteed to converge to anything, lest alone necessarily a global or even local optimum of the original problem. Even if it does converge, the iterates are not necessarily monotonically improving.
Yes, I use SCA in both the objective function and the constraint conditions. These are the optimal values of the iterative output, that is, cvx _ optval. I am seeking the minimum value of the objective function. I think that as long as the iteration is optimized, the output objective function value will gradually decrease and converge to a value. In the similar program I wrote before, the value of cvx output seems to be monotonous ( less volatile ), but I am not sure whether it is because the complexity of this problem is now rising. The output value fluctuates around the convergence value. Attached is a report of the Mosek solver.
With crude unsafeguarded SCA, sometimes you are lucky, and sometimes you are not. Note that the starting values of the variables in the iteration can play a part in the 'luck".
Thank you for your careful answer, I thought as long as I put the value of the previous cvx as the initial value of the next cvx, the effect will be better and better, but although the results in the early iteration effect is very good, but in the convergence of the time will begin to fluctuate. I think I may need to reduce the size of the problem, because I suspect that it may also be the size of the problem that causes the optimal value to fluctuate.