Is there an issue with your cauchy points finding step?

[cwcw1999]

I am questioning if there is an issue with Step 3 of finding the Cauchy Point.
You are updating the vector 'p' during the loop, but according to the paper,
'p' should remain fixed within a single iteration. I think the correct approach
to updating vector 'p' is to use a temporary vector to record its dynamics and
then add them up outside the loop.

[yixuan]

Thanks. I'll check the details when I get some time.

[yixuan]

Hi, I checked the paper, and it seems that the algorithm indeed updates the $p$ vector in each segment search. Could you explain a little bit more on your point?

[cwcw1999]

While p indeed updates with each segment search, my point is that p should remain fixed during an individual segment search.

where j denotes the current segment index.
However, within a single segment search, p gets updated as each active element changes in the code.

So, I think the correct approach to update p is using a temporary vector to record its dynamics and then add them up outside the loop.

[yixuan]

I think now I more or less get your point.

In a typical setting, there is only one variable becoming active after one segment search. This is how the original paper describes the algorithm:

The paper only briefly mentions the case that multiple variables become active:

My understanding is that Algorithm CP in the original paper is based on the assumption that there is only one active variable, and it is not very clear what to do in the more complex scenario.

My implementation assumes that all variables need to be updated, as long as the active set changes, and in your opinion some vectors such as $p$ should remain fixed within a segment search. Did I describe the problem correctly?

If yes, then I shall look into the math more deeply to see which scheme is more reasonable.

[cwcw1999]

Yes, you described the problem correctly.