I find myself using the word suboptimal quite a lot. In my understanding it is an understatement in itself, as suboptimal is not optimal at all and the subject needs drastic improvements.
I had the same question and problems looking up meanings in dictionaries :)
https://german.stackexchange.com/questions/1961/what-is-a-suboptimal-question
Because of its ambiguous, often ironic meaning, i wouldnt recommend to use it in academic papers, you should prefer exact terms here imo. Someone not used to latin terms and special connotations of it in his native language might misunderstand you.
Concerning simchona answer: it is widely used, yes, but more directly next and together with optimal, then its literal meaning is clear contrary to ironic usage in spoken language.
I still wouldnt recommend to use suboptimal alone implying a absolute meaning (rather than a relative meaning together with optimal) e.g. in this way.
My measurement results were suboptimal.
This is more a ambiguous euphemism than a exact summary.
The word suboptimal is not always considered a word in itself (that is, it is not given its own definition page), but it is understood. Dictionary.com gives the definition which you guessed at, that is:
being below an optimal level or standard.
In the contexts I have heard, the word usually uses its literal meaning. It does normally indicate that something is lower than optimal, enough to be noticeable. However, it does not have to be a gross overstatement--especially not in academic works.
The authoritative Oxford English Dictionary includes suboptimal on its page about the prefix "sub", noting that it has been used since 1901 in academic journals:
1901 Amer. Jrnl. Physiol. 4 477 If the stimulation is *sub-optimal, the animal will seek the source of light.
1980 Sci. Amer. Sept. 134/1 On the whole, however, India remains a case of stunted, suboptimal growth, burdened as it is with the world's largest single national mass of poverty and unemployment.
Because of where this phrase has been used, I would say it is perfectly fine for usage in an academic or semi-academic paper. You can write it "sub-optimal" to emphasize that "sub-" is the prefix, or "suboptimal".
The prefix "sub" means "under, below". If I heard "sub-logical" I would assume that it meant something less than logical. It would be interpreted correctly, and you could technically coin any term with a prefix that you wanted. There are no "rules" for what you can pair "sub-" with, as far as I know.
"Suboptimal" means that the solution is not the best. As far as hyperbole (using it to mean that something is not nearly the best and needs improvement), that depends on context and the same rules that apply to any such comment of that style apply.
For a "semi-academic" paper, I cannot speak to appropriate usage, as I am not familiar with the style. However, if you are using this term in an academic context, it is best to be exact. In other words, you should use this term to say that something is not the best. If you want to say that something needs improvement, this is accurate, but it does not convey such meaning in an academic context, and you should specify that the expected standards are not met.
The term "suboptimal" can be applied to any adjective where another adjective would better serve the purpose. It could most definitely be applied to "sub-logical", as "illogical" is better.
As far as "sub-optimal" being correct, I can't say. I, personally, would use "suboptimal" rather than "sub-optimal", but I think that may just be a style choice.
The OED reports that suboptimal means "less than the optimal; not of the best sort or quality." It doesn't mean it's very lower than the optimal.
