Roundup contains a water soluble herbicide glyphosate. The mature leaves of Algerian ivy have a very waxy surface which prevents the herbicide from entering the plant tissue.
A non-chemical way to get rid of ivy is to cut back the above-ground leaves and stems and then dig out as many of the large roots and stems as possible. Water the soil periodically and dig out any new shoots that grow back from underground stems.
If you want to use Roundup or another herbicide on ivy, apply it on new light-green leaves that are about 2/3 size of mature foliage. This new growth will absorb more herbicide than mature leaves. You may have more success using the herbicide triclopyr (Ortho Brush-B-Gon) which is more effective than Roundup on most woody plants.
For more information see UC Pest Note 74142 Woody Weed Invaders,
By V. Lazaneo, Urban Horticulture Advisor, Emeritus, UC Cooperative Extension August 2012