Simple is usually fastest in perl.

#! perl -slw
use strict;
use List::Util qw[ max ];

my %maxs;
$maxs{ $. } = max m[(\d+)]g while <DATA>;

print "line: $_ max: $maxs{ $_ }" for sort keys %maxs;

__DATA__
ASBSDEC 34 GADVVEEVEETTE 56 IOEOREAK GKJEOG EFEAF 1090 DAFFEE 376
ASB C 134 PPKOREAK EFEAF 290
A 100 B 1000 C 2000 D 3000 E 4000  F 5000 G 6000 H 7000 I 8000 J 9000 
+K 10000 L 100000 M 200000 N 2
[download]

Output:

c:\test>junk4
line: 1 max: 1090
line: 2 max: 290
line: 3 max: 200000
[download]

Update: Using an array for output presentation, instead of a hash (as implied by ysth++ below):

#! perl -slw
use strict;
use List::Util qw[ max ];

my @maxs;
$maxs[ $. ] = max m[(\d+)]g while <DATA>;

print "line: $_ max: $maxs[ $_ ]" for 1 .. $#maxs;

__DATA__
ASBSDEC 34 GADVVEEVEETTE 56 IOEOREAK GKJEOG EFEAF 1090 DAFFEE 376
ASB C 134 PPKOREAK EFEAF 290
A 100 B 1000 C 2000 D 3000 E 4000  F 5000 G 6000 H 7000 I 8000 J 9000 
+K 10000 L 100000 M 200000 N 2
[download]