Geometric optimization is a branch of optimization theory that focuses on finding the best solution to mathematical problems involving geometric structures. This may include finding the optimal arrangement of points, lines, shapes, or surfaces in space, while satisfying certain constraints or objectives. Geometric optimization is widely applicable in various fields such as computer graphics, robotics, computer-aided design, operations research, and computational geometry. Researchers in this area develop algorithms and techniques to efficiently solve geometric optimization problems, often using tools from convex optimization, linear programming, and computational geometry. Overall, the goal of geometric optimization research is to develop efficient and effective methods for solving optimization problems that involve geometric structures and relationships.