The Free On-line Dictionary of Computing (30 December 2018):

search problem

    A computational problem that requires
   identifying a solution from some, possibly infinite, solution
   space (set of possible solutions).  E.g. "What is the
   millionth prime number?".  This contrasts with a decision
   problem which merely asks whether a given answer is a
   solution or not.

   (1999-02-15)