I just came across this algorithm in an engineering paper in which I believe the author claims It guarantees global optimality in non-linear systems but never mentioned the convexity of the problem. Is there any algorithm that would find a global optimum in a non-convex problem?
https://ieeexplore.ieee.org/document/100728
The remark is made in the fourth paragraph of the introduction section:
Second, the homotopy method is globally convergent, i.e., one may choose any initial guesses and the homotopy method is guaranteed to converge to all solutions with probability one. However, for large-scale load flow problems, homotopy method requires exponential increase important in the computing capability.