A geometric optimization problem is an optimization problem induced by a set of geometric objects. Geometric algorithms meant for optimization problems have many applications. They are studied both from a theoretical point of view in computational geometry and from the applied point of view in operations research, robotics, graphs or geographical information systems. The focus in computational geometry is efficient algorithms (exact or approximate) for abstract versions of problems. Nevertheless, the problems in some applied areas are not so abstract and heuristic algorithms are sufficient without a formal proof of their goodness.

Formulations and geometrical resolutions are well-known for many decision and optimization problems in service location, data mining, shape recognition, etc. Within this research line, optimization problems are addressed by exploring its resolution from several points of view, and by proving the approximate solution factor when it applies. Geometric optimization problems are normally NP-hard. In such a case, both heuristics and approximation algorithms are explored. The research in this area is focused on three classes of problems that come from three emergent applied areas. These areas contain a great variety of problems, all of them having both theoretical and practical interest. Therefore, the main goal in this project is to develop the knowledge of this kind of problems and their resolution, by using the existing synergy between computational geometry and operations research.