my $pat = join '|', @dates;
my @files = grep /$pat/, @logfiles;
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But I have no idea if that would be faster or slower than just doing a nested loop. A nested loop at least gives you the option of skipping the remainder when you've found a match.

my @files;
foreach my $file( @logfiles ) { 
    foreach my $date( @dates ) { 
        if ( $file =~ /$date/ ) { 
            push @files, $file; 
            last;
        }
    }
}
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