What to do when the claims in a paper are proven to be wrong?

Write a paper explaining what the errors are and how they invalidate the results of the papers in question, then submit it to a journal with good visibility and get it published. Writing directly to the journal editors is appropriate only if you have good evidence that the errors in question are deliberate (e.g., the authors have fabricated data in order to obtain the results they wanted).

I have mathematically proven that the central assumptions and claims in that series of papers were wrong and/or incomplete.

This is a very complicated statement and it is important to understand it in order to know what to do. The two issues are assumptions and claim.

People often make assumptions to solve difficult research problems under the assumed conditions. If your assumptions are too extreme, or worse known to be wrong, then no one will care about your solution. The key issue, however, is that if someone later proves that your assumptions were wrong this does not make your results wrong. It just means that the conditions for which you solved the problem are uninteresting.

Given a set of assumptions, regardless of if they are true or untrue, claims based on those assumptions can be correct, incorrect or incomplete. If in a further investigation you realize that the claims are incorrect or incomplete, or the assumptions needed to obtain the claims are either incomplete (i.e., you need additional assumptions) or incorrect (i.e., the wrong assumption was made not an assumption that was wrong). In these cases there is an issue with the research that should be corrected. Most journals have mechanisms for correcting errors or at least alerting readers to errors.

The concept of proving an assumption to be wrong is a strange idea. An assumption is an idea that you take to be true while an idea that will be subjected to testing is generally called a hypothesis (or in mathematics I believe a conjecture). Taking someone else's assumption and hypothesizing that it is true (or false) and then testing that can be very valuable research. Proving that the assumed conditions do not occur reduces the importance of the previous research that assumes the conditions occur, but it does not change whether that previous research is correct or incorrect. In this case you need to decide if the proof that the conditions do not occur is interesting enough to publish.

Basically there's nothing you can do. I had exactly the same experience with a paper written by some Ivy League computer scientists whose algrotihm I was supposed to implement. Their papers contained no information about how they chose the starting points for their optimization, which was a serious problem because there were many local maxima. They had written a software package but it had been withdrawn from circulation.

I discussed my problems with other researchers in the field and was told that it's generally known that "there are problems with that paper." That's as far as it goes, really. It would be nice if there was some way of calling them to account for wasting peoples' time and making claims that they couldn't substantiate, but there's really nothing you can do.