I am trying to solve a constrained optimization problem using filter methods and came across two papers on the topic that I am having some problems with. The original filter method paper is the following: Fletcher & Leyffer (2002) and the paper I am trying to compare it against is Pericaro, et al (2013).

Now, where I am struggling is with convincing myself that the two algorithms outlined are the same thing (I think they are not, but I was told that is not the case).

More specifically, I want to know if the Algorithm 1 in both papers produce the same filter result. I am completely comfortable with the Fletcher and Leyffer idea of the filter, but when I read the Pericaro paper I have no idea how they are keeping track of the points.

For example, Fletcher and Leyffer say that we add a point $x^{k+1}$ to the filter if it belongs to the set of all non-dominated points. That's easy to check but (in my mind) requires looking at both $f$ and $h$.

However, in the Pericaro paper, their filter update step in Algorithm 1 only checks that $f(x^{k+1})<f(x^k)$. Don't we need to also check some condition on $h$ as well?

This is where I am confused more so, is understanding Pericaro's Algorithm 1.