Geometric optimization is a field of mathematics and computer science focused on finding the best possible solution to problems involving geometric shapes and spaces. This can include maximizing areas, minimizing distances, or optimizing the arrangement of objects. Techniques often involve algorithms that analyze the properties of shapes and their relationships in a given space. Applications of geometric optimization are widespread, including in fields like robotics, computer graphics, and operations research. For example, it can help in designing efficient paths for robots or optimizing layouts in manufacturing to reduce waste and improve productivity.