Trachelospermum asiaticum

Trachelospermum asiaticum is a durable vine or ground-cover plant with fragrant white flowers in the spring. It grows in sun or shade, and is drought-tolerant once established.
It makes a nice evergreen ground-cover that can be mowed short a couple of times a year if it starts looking unkempt. The dense growth will prevent most weeds from sprouting, and provides excellent erosion control on slopes. This plant is also a good low-maintenance grass alternative for your lawn. The semi-woody stems can spread beyond the area where they're planted, so you may want to surround the planting bed with landscape edging to keep it in bounds.

Flowering will be best on stems that are allowed to vine up, or drape over some other object. The 2-inch long leaves are a dark glossy green, and have a leathery texture.
Trachelospermum asiaticum is not a true jasmine, but is sometimes called Yellow Star jasmine, or more commonly, Asiatic jasmine. It is native to Korea and Japan, and is recommended for USDA Zones 8-10.
There are some cultivars available with variegated or bronze foliage.