Is there a log file that logs information when the values set in
/etc/security/limits.conf are exceeded?
If not is there a way to make it log when the values are exceeded?
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There is no central log for every process that hits these limits.
Whenever a process tries to allocate resources which exceed it's limit, it receives a negative return code from the OS, so each process can handle this case in it's own way. Most processes will write something into their specific log if they hit one of the limits, but you'll have to check that for each process specifically.
I have been able to achieve partial solution using audit subsystem. The idea is to track the failed system calls.
You may refer  to track the work I have done in this field.
As per man limit page
The pam_limits module does report configuration problems found in its configuration file and errors via syslog(3).
So you need to define as below
pam_limits.so [ conf=/path/to/limits.conf ] [ debug ] [ set_all ] [ utmp_early ] [ noaudit ]
Example of my
session required pam_limits.so conf=/etc/security/limits.conf