lookup min value in ranges of dates

I've attached a workbook which has two columns of dates. The first column (A) contains a continuous series of dates. Next to each date (Column B) is a value (a percentage) from a database.

The second column of dates is not continuous. It is broken into ranges of dates (Column J), each one associated with a Ticket # (Column K).

For each range of dates associated with a ticket number I need to find the minimum value in column B.

I've manually calculated some desired results in column W.

Can someone help me with the formula for this? Thanks so much!

Thanks Ben, that works! I just drug column Z over to column W, and the formulas held together. I appreciate this.

Hi, after I tried these formulas in my actual workbook they didn't always function correctly.

Flameretired, I settled on your formula for now though. I've attached it in a facsimile of my actual workbook so that
we can use the actual column letters in an effort to reduce the possibility that I am making a mistake when I
put the formula to use.

If you scroll down to rows 711 through 781, you'll see three sets of ranges with their respective IDs (#123610 through
#123612).

The formula result is incorrect with these IDs. You'll see that in each case it is showing -3.15%. The correct
solutions are shown in column BP.

I thought that creating absolute ranges might help (e.g. $T$47:$T$2000) but this didn't work.

Any suggestions?

Thanks

Please try at BO47

=IF(BH47<>"",MIN(AT47:INDEX(AT47:$AT$9999,MATCH(BH47,BG47:BG$9999)),0),"")

Thanks Bo_Ry, that works!