I don't think there is any contradiction between being a problem-solver and having a positive outlook on life, as long as you are a competent problem solver and getting a lot of problems solved. Successful problem solving provides both an immediate joy from a "mission accomplished" feeling, and a long term positive outlook that comes with the feeling that because of you, there are less unsolved problems in the world, therefore life is better.
Don`t people become problem-solvers because they enjoy solving problems? And if that is a case, than being presented with a host of unsolved, yet potentially solvable problems should make a problem-solver scream with glee, right?