We often hear people concerned not to raise "false hope" among other people. If the intent is not to lead people to waste their time or efforts or money, I agree. For example, if someone thinks they are getting into Oxford but in fact have no chance, then it makes no sense to sell your house and move to England because you believe you are getting into Oxford. In the legal world, we refer to such costs as "detrimental reliance"--your false hope has led you to rely on an illusion that is incurring real and major costs, not just direct costs but the indirect opportunity cost of foregoing more promising alternatives.
But optimism is not false hope when there are no such costs involved. And, often, there are situations where optimism imposes no major direct or opportunity costs or just imposes trivial costs. Let's take an example from the social world. For some of us with Latin backgrounds, the coldness of American culture is amazing. We see people ignore so many opportunities for friendly interactions with others that impose no costs at all: no significant costs and, perhaps, a great benefit, such as a job offer, a future recommendation, a friendship, or even romance. Yet, people bypass such opportunities all of the time by being aloof from others around them, even those others whom they see often and with whom they interact frequently, to some degree or other. The optimistic approach would be to simply be a warm and friendly person because of all the potential benefits involved.
Of course, if you have a warm and friendly personality, you will do this anyway. But, if you need some extra motivation, then do a rational "optimist" analysis as above. The same analysis is applicable to many other situations: what are the direct and opportunity costs of doing something? What are the potential benefits? And then be optimistic in your approach, because it is rational to be so!