SQL Server Index and Statistics Maintenance performance question
Can somebody share with me his experience in using IndexOptimize for a
  database with a very high number of indexes ?


You are right, Ola's script first gets data from all the index related DMV's and inserts them inside of @tmpIndexesStatistics, even if one table or one index is specified.
For a lot of indexes, it gets stuck on this first command, which is a fairly huge query. See below for the query and even further below for a possible fix for this.



TL;DR 

In one of the queries, the dynamic management views are called a couple of times each with multiple filters. 

All this results in a fairly big execution plan.

Creating temp tables and storing the data from the DMV's prior to running the query is a workaround. You could optimize further with indexes on these temp tables / Rewrites.

Test data: >100K empty tables + >200k empty indexes

USE Test2
GO
SET NOCOUNT ON;
DECLARE @SQL NVARCHAR(MAX)
DECLARE @i int = 0

DECLARE @counter int = 1000
WHILE @i &lt;+ @counter
BEGIN
SET @SQL = N'CREATE TABLE dbo.'+QUOTENAME(cast(@i as nvarchar(20)))+'( id int, val varchar(255));'
EXEC(@sql)
SET @SQL = N'CREATE INDEX IX_'+cast(@i as nvarchar(20))+ ' ON '+QUOTENAME(cast(@i as nvarchar(20)))+'(id) '
EXEC(@sql)
SET @SQL = N'CREATE INDEX IX_'+cast(@i as nvarchar(20))+ '_2 ON '+QUOTENAME(cast(@i as nvarchar(20)))+'(val) '
EXEC(@sql)
set @I +=1

IF @i = @counter
BEGIN

  IF @counter &lt; 100000
  BEGIN
        SET @counter += 1000;
  END
END
END

select count(*) from sys.tables;
--100731

select count(*) from sys.indexes  where index_id != 0;
--201614


When changing the parameters to  work on all the indexes, and printing instead of executing the statement ( @Execute='N') 

EXECUTE MNGDB.dbo.IndexOptimize
@Databases = 'test2',
@Indexes =  'test2.dbo.',
@FragmentationLow = NULL,
@FragmentationMedium = 'INDEX_REORGANIZE,INDEX_REBUILD_ONLINE,INDEX_REBUILD_OFFLINE',
@FragmentationHigh = 'INDEX_REBUILD_ONLINE,INDEX_REBUILD_OFFLINE',
@FragmentationLevel1 = 30,
@FragmentationLevel2 = 50,
@UpdateStatistics = 'ALL',
@OnlyModifiedStatistics = 'Y',
@LogToTable = 'Y',
@LockTimeout = 60,
@Execute='N';


This huge query comes into play

SET TRANSACTION ISOLATION LEVEL READ UNCOMMITTED;
USE [test2]; 
SELECT SchemaID, SchemaName, ObjectID, ObjectName, ObjectType, IsMemoryOptimized, IndexID, IndexName, IndexType, AllowPageLocks, IsImageText, IsNewLOB, IsFileStream, IsColumnStore, IsComputed, IsTimestamp, OnReadOnlyFileGroup, ResumableIndexOperation, StatisticsID, StatisticsName, NoRecompute, IsIncremental, PartitionID, PartitionNumber, PartitionCount, [Order], Selected, Completed 
FROM (SELECT schemas.[schema_id] AS SchemaID, schemas.[name] AS SchemaName, objects.[object_id] AS ObjectID, objects.[name] AS ObjectName, RTRIM(objects.[type]) AS ObjectType, tables.is_memory_optimized AS IsMemoryOptimized, indexes.index_id AS IndexID, indexes.[name] AS IndexName, indexes.[type] AS IndexType, indexes.allow_page_locks AS AllowPageLocks, 
CASE WHEN indexes.[type] = 1 AND EXISTS(SELECT * FROM sys.columns columns INNER JOIN sys.types types ON columns.system_type_id = types.user_type_id WHERE columns.[object_id] = objects.object_id AND types.name IN('image','text','ntext')) THEN 1 ELSE 0 END AS IsImageText, 
CASE WHEN indexes.[type] = 1 AND EXISTS(SELECT * FROM sys.columns columns INNER JOIN sys.types types ON columns.system_type_id = types.user_type_id OR (columns.user_type_id = types.user_type_id AND types.is_assembly_type = 1) WHERE columns.[object_id] = objects.object_id AND (types.name IN('xml') OR (types.name IN('varchar','nvarchar','varbinary') AND columns.max_length = -1) OR (types.is_assembly_type = 1 AND columns.max_length = -1))) THEN 1 WHEN indexes.[type] = 2 
            AND EXISTS(SELECT * FROM sys.index_columns index_columns INNER JOIN sys.columns columns ON index_columns.[object_id] = columns.[object_id] 
            AND index_columns.column_id = columns.column_id 
            INNER JOIN sys.types types ON columns.system_type_id = types.user_type_id OR (columns.user_type_id = types.user_type_id AND types.is_assembly_type = 1) WHERE index_columns.[object_id] = objects.object_id AND index_columns.index_id = indexes.index_id AND (types.[name] IN('xml') OR (types.[name] IN('varchar','nvarchar','varbinary') AND columns.max_length = -1) OR (types.is_assembly_type = 1 AND columns.max_length = -1))) 
            THEN 1 ELSE 0 END AS IsNewLOB, 
CASE WHEN indexes.[type] = 1 AND EXISTS(SELECT * FROM sys.columns columns WHERE columns.[object_id] = objects.object_id  AND columns.is_filestream = 1) THEN 1 ELSE 0 END AS IsFileStream, 
CASE WHEN EXISTS(SELECT * FROM sys.indexes indexes WHERE indexes.[object_id] = objects.object_id AND [type] IN(5,6)) THEN 1 ELSE 0 END AS IsColumnStore, 
CASE WHEN EXISTS(SELECT * FROM sys.index_columns index_columns INNER JOIN sys.columns columns ON index_columns.object_id = columns.object_id AND index_columns.column_id = columns.column_id WHERE (index_columns.key_ordinal &gt; 0 OR index_columns.partition_ordinal &gt; 0) AND columns.is_computed = 1 AND index_columns.object_id = indexes.object_id AND index_columns.index_id = indexes.index_id) THEN 1 ELSE 0 END AS IsComputed, 
CASE WHEN EXISTS(SELECT * FROM sys.index_columns index_columns INNER JOIN sys.columns columns ON index_columns.[object_id] = columns.[object_id] AND index_columns.column_id = columns.column_id INNER JOIN sys.types types ON columns.system_type_id = types.system_type_id 
WHERE index_columns.[object_id] = objects.object_id AND index_columns.index_id = indexes.index_id AND types.[name] = 'timestamp') THEN 1 ELSE 0 END AS IsTimestamp, 
CASE WHEN EXISTS (SELECT * FROM sys.indexes indexes2 INNER JOIN sys.destination_data_spaces destination_data_spaces ON indexes.data_space_id = destination_data_spaces.partition_scheme_id INNER JOIN sys.filegroups filegroups ON destination_data_spaces.data_space_id = filegroups.data_space_id WHERE filegroups.is_read_only = 1 AND indexes2.[object_id] = indexes.[object_id] AND indexes2.[index_id] = indexes.index_id AND destination_data_spaces.destination_id = partitions.partition_number) THEN 1 WHEN EXISTS (SELECT * FROM sys.indexes indexes2 INNER JOIN sys.filegroups filegroups ON indexes.data_space_id = filegroups.data_space_id WHERE filegroups.is_read_only = 1 AND indexes.[object_id] = indexes2.[object_id] AND indexes.[index_id] = indexes2.index_id) THEN 1 WHEN indexes.[type] = 1 AND EXISTS (SELECT * FROM sys.tables tables INNER JOIN sys.filegroups filegroups ON tables.lob_data_space_id = filegroups.data_space_id WHERE filegroups.is_read_only = 1 AND tables.[object_id] = objects.[object_id]) THEN 1 ELSE 0 END AS OnReadOnlyFileGroup, CASE WHEN EXISTS(SELECT * FROM sys.index_resumable_operations index_resumable_operations WHERE state_desc = 'PAUSED' AND index_resumable_operations.object_id = indexes.object_id AND index_resumable_operations.index_id = indexes.index_id AND (index_resumable_operations.partition_number = partitions.partition_number OR index_resumable_operations.partition_number IS NULL)) THEN 1 ELSE 0 END AS ResumableIndexOperation, stats.stats_id AS StatisticsID, stats.name AS StatisticsName, stats.no_recompute AS NoRecompute, stats.is_incremental AS IsIncremental, partitions.partition_id AS PartitionID, partitions.partition_number AS PartitionNumber, IndexPartitions.partition_count AS PartitionCount, 0 AS [Order], 0 AS Selected, 0 AS Completed FROM sys.indexes indexes INNER JOIN sys.objects objects ON indexes.[object_id] = objects.[object_id] INNER JOIN sys.schemas schemas ON objects.[schema_id] = schemas.[schema_id] LEFT OUTER JOIN sys.tables tables ON objects.[object_id] = tables.[object_id] LEFT OUTER JOIN sys.stats stats ON indexes.[object_id] = stats.[object_id] AND indexes.[index_id] = stats.[stats_id] LEFT OUTER JOIN sys.partitions partitions ON indexes.[object_id] = partitions.[object_id] AND indexes.index_id = partitions.index_id LEFT OUTER JOIN (SELECT partitions.[object_id], partitions.index_id, COUNT(DISTINCT partitions.partition_number) AS partition_count FROM sys.partitions partitions GROUP BY partitions.[object_id], partitions.index_id) IndexPartitions ON partitions.[object_id] = IndexPartitions.[object_id] AND partitions.[index_id] = IndexPartitions.[index_id] WHERE objects.[type] IN('U','V') AND objects.is_ms_shipped = 0 AND indexes.[type] IN(1,2,3,4,5,6,7) AND indexes.is_disabled = 0 AND indexes.is_hypothetical = 0 

UNION 

SELECT schemas.[schema_id] AS SchemaID, schemas.[name] AS SchemaName, objects.[object_id] AS ObjectID, objects.[name] AS ObjectName, RTRIM(objects.[type]) AS ObjectType, tables.is_memory_optimized AS IsMemoryOptimized, NULL AS IndexID, NULL AS IndexName, NULL AS IndexType, NULL AS AllowPageLocks, NULL AS IsImageText, NULL AS IsNewLOB, NULL AS IsFileStream, NULL AS IsColumnStore, NULL AS IsComputed, NULL AS IsTimestamp, NULL AS OnReadOnlyFileGroup, NULL AS ResumableIndexOperation, stats.stats_id AS StatisticsID, stats.name AS StatisticsName, stats.no_recompute AS NoRecompute, stats.is_incremental AS IsIncremental, NULL AS PartitionID, dm_db_incremental_stats_properties.partition_number AS PartitionNumber, NULL AS PartitionCount, 0 AS [Order], 0 AS Selected, 0 AS Completed FROM sys.stats stats INNER JOIN sys.objects objects ON stats.[object_id] = objects.[object_id] INNER JOIN sys.schemas schemas ON objects.[schema_id] = schemas.[schema_id] LEFT OUTER JOIN sys.tables tables ON objects.[object_id] = tables.[object_id] OUTER APPLY sys.dm_db_incremental_stats_properties(stats.object_id, stats.stats_id) dm_db_incremental_stats_properties WHERE objects.[type] IN('U','V') AND objects.is_ms_shipped = 0 AND NOT EXISTS(SELECT * FROM sys.indexes indexes WHERE indexes.[object_id] = stats.[object_id] AND indexes.index_id = stats.stats_id)) IndexesStatistics


Now, when we try to find what triggers this command inside [dbo].[IndexOptimize]

IF EXISTS(SELECT * FROM @ActionsPreferred) OR @UpdateStatistics IN('ALL','INDEX')


With @ActionsPreferred corresponding to the fragmentationlevel actions and @UpdateStatistics being update statistics. Meaning that it will run whenever we do a stat update or a index rebuild / reorganize.

no filtering is applied, the query runs over all the indexes in the database.

As a result, at the moment we will have to go through all that trouble, even if we specify one table.

EXECUTE MNGDB.dbo.IndexOptimize
@Databases = 'test2',
@Indexes =  'test2.dbo.[83631]',
@FragmentationLow = NULL,
@FragmentationMedium = 'INDEX_REORGANIZE,INDEX_REBUILD_ONLINE,INDEX_REBUILD_OFFLINE',
@FragmentationHigh = 'INDEX_REBUILD_ONLINE,INDEX_REBUILD_OFFLINE',
@FragmentationLevel1 = 30,
@FragmentationLevel2 = 50,
@UpdateStatistics = 'ALL',
@OnlyModifiedStatistics = 'Y',
@LogToTable = 'Y',
@LockTimeout = 60,
@EXECUTE= 'N'




The actual index filtering happen after the the huge command runs:

IF @Indexes IS NULL
      BEGIN
        UPDATE tmpIndexesStatistics
        SET tmpIndexesStatistics.Selected = 1
        FROM @tmpIndexesStatistics tmpIndexesStatistics
      END
      ELSE
      BEGIN
...


and updates the tmpIndexesStatistics table accordingly, as to execute index operations on these indexes.

This query was running over 60 minutes on my small dev server before killing it.



What could possibly be a fix for this?

Well, you would have to change ola's script, but a solution with temp tables worked for me, and executed in 1 minute. Without a doubt, it could be optimized further:

SET TRANSACTION ISOLATION LEVEL READ UNCOMMITTED;
USE [test2]; 

select * 
INTO #Indexes
from sys.indexes;


select *  
INTO #Index_columns
FROM sys.index_columns;

SELECT * 
INTO #columns
FROM SYS.columns;

SELECT * 
INTO #types 
FROM
sys.types;

SELECT *
INTO #destination_data_spaces
FROM sys.destination_data_spaces;


SELECT *
INTO #filegroups
FROM sys.filegroups;


SELECT *
INTO #stats
FROM sys.stats;

SELECT *
INTO #objects
FROM sys.objects;


SELECT *
INTO #partitions
FROM sys.partitions;


SELECT *
INTO #tables
FROM sys.tables;


SELECT *
INTO #index_resumable_operations
FROM sys.index_resumable_operations 

SELECT *
INTO #schemas
FROM sys.schemas 

+ rerun the query with temp tables instead (char limit)


To change this in the index optimization procedure

Sorry Ola this will hurt to look at

When I scripted the proc, this was from line 1430 Until 1537

 IF DATABASEPROPERTYEX(@CurrentDatabaseName,'Status') = 'ONLINE'
    AND (@CurrentIsDatabaseAccessible = 1 OR @CurrentIsDatabaseAccessible IS NULL)
    AND DATABASEPROPERTYEX(@CurrentDatabaseName,'Updateability') = 'READ_WRITE'
    BEGIN

      -- Select indexes in the current database
      IF (EXISTS(SELECT * FROM @ActionsPreferred) OR @UpdateStatistics IS NOT NULL) AND (GETDATE() &lt; DATEADD(ss,@TimeLimit,@StartTime) OR @TimeLimit IS NULL)
      BEGIN
        SET @CurrentCommand01 = 'SET TRANSACTION ISOLATION LEVEL READ UNCOMMITTED;'
                              + 'USE ' + QUOTENAME(@CurrentDatabaseName) + ';
                                select * 
                                INTO #Indexes
                                from sys.indexes;
                                select *  
                                INTO #Index_columns
                                FROM sys.index_columns;
                                SELECT * 
                                INTO #columns
                                FROM SYS.columns;
                                SELECT * 
                                INTO #types 
                                FROM
                                sys.types;
                                SELECT *
                                INTO #destination_data_spaces
                                from sys.destination_data_spaces;
                                SELECT *
                                INTO #filegroups
                                FROM sys.filegroups;
                                SELECT * kill 64
                                INTO #stats
                                from sys.stats;
                                SELECT *
                                INTO #objects
                                from sys.objects;       
                                SELECT *
                                INTO #partitions
                                from sys.partitions;
                                SELECT *
                                INTO #tables
                                FROM sys.tables;
                                SELECT *
                                INTO #index_resumable_operations
                                FROM sys.index_resumable_operations;
                                SELECT *
                                INTO #schemas
                                FROM sys.schemas; '
                              + ' SELECT SchemaID, SchemaName, ObjectID, ObjectName, ObjectType, IsMemoryOptimized, IndexID, IndexName, IndexType, AllowPageLocks, IsImageText, IsNewLOB, IsFileStream, IsColumnStore, IsComputed, IsTimestamp, OnReadOnlyFileGroup, ResumableIndexOperation, StatisticsID, StatisticsName, NoRecompute, IsIncremental, PartitionID, PartitionNumber, PartitionCount, [Order], Selected, Completed'
                              + ' FROM ('

        IF EXISTS(SELECT * FROM @ActionsPreferred) OR @UpdateStatistics IN('ALL','INDEX')
        BEGIN
          SET @CurrentCommand01 = @CurrentCommand01 + 'SELECT schemas.[schema_id] AS SchemaID'
                                                    + ', schemas.[name] AS SchemaName'
                                                    + ', objects.[object_id] AS ObjectID'
                                                    + ', objects.[name] AS ObjectName'
                                                    + ', RTRIM(objects.[type]) AS ObjectType'
                                                    + ', ' + CASE WHEN @Version &gt;= 12 THEN 'tables.is_memory_optimized' ELSE '0' END + ' AS IsMemoryOptimized'
                                                    + ', indexes.index_id AS IndexID'
                                                    + ', indexes.[name] AS IndexName'
                                                    + ', indexes.[type] AS IndexType'
                                                    + ', indexes.allow_page_locks AS AllowPageLocks'

                                                    + ', CASE WHEN indexes.[type] = 1 AND EXISTS(SELECT * FROM #columns columns INNER JOIN #types types ON columns.system_type_id = types.user_type_id WHERE columns.[object_id] = objects.object_id AND types.name IN(''image'',''text'',''ntext'')) THEN 1 ELSE 0 END AS IsImageText'

                                                    + ', CASE WHEN indexes.[type] = 1 AND EXISTS(SELECT * FROM #columns columns INNER JOIN #types types ON columns.system_type_id = types.user_type_id OR (columns.user_type_id = types.user_type_id AND types.is_assembly_type = 1) WHERE columns.[object_id] = objects.object_id AND (types.name IN(''xml'') OR (types.name IN(''varchar'',''nvarchar'',''varbinary'') AND columns.max_length = -1) OR (types.is_assembly_type = 1 AND columns.max_length = -1))) THEN 1'
                                                    + ' WHEN indexes.[type] = 2 AND EXISTS(SELECT * FROM #Index_columns index_columns INNER JOIN #columns columns ON index_columns.[object_id] = columns.[object_id] AND index_columns.column_id = columns.column_id INNER JOIN #types types ON columns.system_type_id = types.user_type_id OR (columns.user_type_id = types.user_type_id AND types.is_assembly_type = 1) WHERE index_columns.[object_id] = objects.object_id AND index_columns.index_id = indexes.index_id AND (types.[name] IN(''xml'') OR (types.[name] IN(''varchar'',''nvarchar'',''varbinary'') AND columns.max_length = -1) OR (types.is_assembly_type = 1 AND columns.max_length = -1))) THEN 1 ELSE 0 END AS IsNewLOB'

                                                    + ', CASE WHEN indexes.[type] = 1 AND EXISTS(SELECT * FROM #columns columns WHERE columns.[object_id] = objects.object_id  AND columns.is_filestream = 1) THEN 1 ELSE 0 END AS IsFileStream'

                                                    + ', CASE WHEN EXISTS(SELECT * FROM #Indexes indexes WHERE indexes.[object_id] = objects.object_id AND [type] IN(5,6)) THEN 1 ELSE 0 END AS IsColumnStore'

                                                    + ', CASE WHEN EXISTS(SELECT * FROM #Index_columns index_columns INNER JOIN #columns columns ON index_columns.object_id = columns.object_id AND index_columns.column_id = columns.column_id WHERE (index_columns.key_ordinal &gt; 0 OR index_columns.partition_ordinal &gt; 0) AND columns.is_computed = 1 AND index_columns.object_id = indexes.object_id AND index_columns.index_id = indexes.index_id) THEN 1 ELSE 0 END AS IsComputed'

                                                    + ', CASE WHEN EXISTS(SELECT * FROM #Index_columns index_columns INNER JOIN #columns columns ON index_columns.[object_id] = columns.[object_id] AND index_columns.column_id = columns.column_id INNER JOIN #types types ON columns.system_type_id = types.system_type_id WHERE index_columns.[object_id] = objects.object_id AND index_columns.index_id = indexes.index_id AND types.[name] = ''timestamp'') THEN 1 ELSE 0 END AS IsTimestamp'

                                                    + ', CASE WHEN EXISTS (SELECT * FROM #Indexes indexes2 INNER JOIN #destination_data_spaces destination_data_spaces ON indexes.data_space_id = destination_data_spaces.partition_scheme_id INNER JOIN #filegroups filegroups ON destination_data_spaces.data_space_id = filegroups.data_space_id WHERE filegroups.is_read_only = 1 AND indexes2.[object_id] = indexes.[object_id] AND indexes2.[index_id] = indexes.index_id' + CASE WHEN @PartitionLevel = 'Y' THEN ' AND destination_data_spaces.destination_id = partitions.partition_number' ELSE '' END + ') THEN 1'
                                                    + ' WHEN EXISTS (SELECT * FROM #Indexes indexes2 INNER JOIN #filegroups filegroups ON indexes.data_space_id = filegroups.data_space_id WHERE filegroups.is_read_only = 1 AND indexes.[object_id] = indexes2.[object_id] AND indexes.[index_id] = indexes2.index_id) THEN 1'
                                                    + ' WHEN indexes.[type] = 1 AND EXISTS (SELECT * FROM #tables tables INNER JOIN #filegroups filegroups ON tables.lob_data_space_id = filegroups.data_space_id WHERE filegroups.is_read_only = 1 AND tables.[object_id] = objects.[object_id]) THEN 1 ELSE 0 END AS OnReadOnlyFileGroup'

                                                    + ', ' + CASE WHEN @Version &gt;= 14 THEN 'CASE WHEN EXISTS(SELECT * FROM #index_resumable_operations index_resumable_operations WHERE state_desc = ''PAUSED'' AND index_resumable_operations.object_id = indexes.object_id AND index_resumable_operations.index_id = indexes.index_id AND (index_resumable_operations.partition_number = partitions.partition_number OR index_resumable_operations.partition_number IS NULL)) THEN 1 ELSE 0 END' ELSE '0' END + ' AS ResumableIndexOperation'

                                                    + ', stats.stats_id AS StatisticsID'
                                                    + ', stats.name AS StatisticsName'
                                                    + ', stats.no_recompute AS NoRecompute'
                                                    + ', ' + CASE WHEN @Version &gt;= 12 THEN 'stats.is_incremental' ELSE '0' END + ' AS IsIncremental'
                                                    + ', ' + CASE WHEN @PartitionLevel = 'Y' THEN 'partitions.partition_id AS PartitionID' WHEN @PartitionLevel = 'N' THEN 'NULL AS PartitionID' END
                                                    + ', ' + CASE WHEN @PartitionLevel = 'Y' THEN 'partitions.partition_number AS PartitionNumber' WHEN @PartitionLevel = 'N' THEN 'NULL AS PartitionNumber' END
                                                    + ', ' + CASE WHEN @PartitionLevel = 'Y' THEN 'IndexPartitions.partition_count AS PartitionCount' WHEN @PartitionLevel = 'N' THEN 'NULL AS PartitionCount' END
                                                    + ', 0 AS [Order]'
                                                    + ', 0 AS Selected'
                                                    + ', 0 AS Completed'
                                                    + ' FROM #Indexes indexes'
                                                    + ' INNER JOIN #objects objects ON indexes.[object_id] = objects.[object_id]'
                                                    + ' INNER JOIN #schemas schemas ON objects.[schema_id] = schemas.[schema_id]'
                                                    + ' LEFT OUTER JOIN #tables tables ON objects.[object_id] = tables.[object_id]'
                                                    + ' LEFT OUTER JOIN #stats stats ON indexes.[object_id] = stats.[object_id] AND indexes.[index_id] = stats.[stats_id]'
          IF @PartitionLevel = 'Y'
          BEGIN
            SET @CurrentCommand01 = @CurrentCommand01 + ' LEFT OUTER JOIN #partitions partitions ON indexes.[object_id] = partitions.[object_id] AND indexes.index_id = partitions.index_id'
                                                      + ' LEFT OUTER JOIN (SELECT partitions.[object_id], partitions.index_id, COUNT(DISTINCT partitions.partition_number) AS partition_count FROM #partitions partitions GROUP BY partitions.[object_id], partitions.index_id) IndexPartitions ON partitions.[object_id] = IndexPartitions.[object_id] AND partitions.[index_id] = IndexPartitions.[index_id]'
          END

          SET @CurrentCommand01 = @CurrentCommand01 + ' WHERE objects.[type] IN(''U'',''V'')'
                                                    + CASE WHEN @MSShippedObjects = 'N' THEN ' AND objects.is_ms_shipped = 0' ELSE '' END
                                                    + ' AND indexes.[type] IN(1,2,3,4,5,6,7)'
                                                    + ' AND indexes.is_disabled = 0 AND indexes.is_hypothetical = 0'
        END


When testing and rerunning the procedure with one table,it executed in one minute:

EXECUTE dbo.IndexOptimize
@Databases = 'test2',
@Indexes =  'test2.dbo.[83631]',
@FragmentationLow = NULL,
@FragmentationMedium = 'INDEX_REORGANIZE,INDEX_REBUILD_ONLINE,INDEX_REBUILD_OFFLINE',
@FragmentationHigh = 'INDEX_REBUILD_ONLINE,INDEX_REBUILD_OFFLINE',
@FragmentationLevel1 = 30,
@FragmentationLevel2 = 50,
@UpdateStatistics = 'ALL',
@OnlyModifiedStatistics = 'Y',
@LogToTable = 'Y',
@LockTimeout = 60,
@EXECUTE= 'N';


Duration      00:01:18

Earlier filters / temp tables with indexes / ... could be used to improve the query further.