This is an ornamental Trachelospermum jasminoides cultivar from Japan. They're valued for their ornamental foliage rather than the flowers and from what I've read are not very floriferous compared to the common green-leafed/white flower Trachelospermum jasminoides (also known as Star Jasmine). I don't think fertilizer would help for yours as it's probably a genetic factor that makes it less inclined to bloom, but it wouldn't hurt to try, just don't over do it of course.

The common star jasmine can be found for under $5/gal from some big box stores. It can grow very fast once established and flowers from March to late Summer if I remember correctly. I love the smell and it's one of those common landscape plants here in So. California that I'm glad is overused. This is a good wafter too.