I was given a paper to build off of for engineering research. The paper was published in a high impact journal but happens to be written very sloppily in the following sense.
The proof of a central result of the paper cites a source which does not have the results that they claim. I found the correct paper which has results that do prove what they claim for their specific case (after writing the proof myself), but the way they wrote their proof heavily suggests that they thought the incorrect paper they cited proved their result. The proof I wrote from the paper I found is drastically different and requires conditions mentioned nowhere in their proof.
They make the claim that their problem can be converted to a linear program. The linear program is very complicated (it involves quadruple and double sums, and a lot of variables), which I believe led the reviewer to be lazy and avoid seriously scrutinizing it. At first I was unsure as to whether there were gaps in my knowledge regarding the setup of the linear program, but after speaking with my advisor he also agreed that as written the linear program does not make sense. I attempted to look later in the paper in the hopes that they rewrote the linear program for their examples but it was not used.
My advisor and I tried looking through their arXiv version in the hopes that maybe the mistake wasn't made there. The linear program they wrote in their arXiv version had even more inconsistencies.
I tried reading through papers that cite this paper (of which there are 70), and everyone either cites their arguments as true or cites the paper because of its contribution.
There is no explanation for the linear program as their "proof" just claims "these equations characterize the variables in the linear program."
Is this worth contacting the journal over? What can be done in this situation?