Knowledge discovery from GPS trajectory data is an important topic in several scientific areas, including data mining, human behavior analysis, and user modeling. This paper proposes a task that assigns personalized visited-POIs. Its goal is to estimate fine-grained and pre-defined locations (i.e., points of interest (POI)) that are actually visited by users and assign visited-location information to the corresponding span of their (personal) GPS trajectories. We also introduce a novel algorithm to solve this assignment task. First, we exhaustively extract stay-points as candidates for significant locations using a variant of a conventional stay-point extraction method. Then we select significant locations and simultaneously assign visited-POIs to them by considering various aspects, which we formulate in integer linear programming. Experimental results conducted on an actual user dataset show that our method achieves higher accuracy in the visited-POI assignment task than the various cascaded procedures of conventional methods.