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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.

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  • $\begingroup$ I'm not very steeped in this field, but was interested enough to read the paper. In Pericaro's algorithm 1, in the step before the filter update it specifically says compute $x^{k+1} \notin \tilde{\mathcal{F}}_k$. But $\tilde{\mathcal{F}}_k$ includes $\mathcal{R}_k$, which is the same thing as saying $x^{k+1}$ is required to be non-dominated I think? Perhaps I am just wildly confused. $\endgroup$
    – David Benson-Putnins
    Commented Nov 26, 2015 at 4:59
  • $\begingroup$ @DavidBenson-Putnins I think you are right. But one of teh largest sources of confusion for me is Pericaro's filter update rules. In particular, she says if $f(x^{k+1})<f(x^k)$ then we discard this point. But isn't that a point you want to keep? $\endgroup$
    – RustyStatistician
    Commented Nov 26, 2015 at 19:14

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