Can I do SEO by Myself?

I am a programmer and have a web marketing team to help me with my website. I would like to know if I can do Search Engine Optimization by myself on my Website. I know the basics of search engine optimizing, but not all of the details. I was wondering if there are any special skills that if I do not know, such as algorithms, that would hurt me if I do the work myself. Should I make a contract with a company to do the work, or since I am a programmer and I know about most of the optimization process, I can do the work myself.