Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a concept that generalizes several different notions of a "centerpoint" in the literature.  develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further,  show that algorithms based on centerpoints are "best possible" in a certain sense. Motivated by this,  establish several structural results about this concept and provide efficient algorithms for computing these points.
['Amitabh Basu', 'Timm Oertel']
I am writing a research paper on a idea Centerpoints: A Link Between Optimization and Convex Geometry
[{"from": "human", "value": "I am writing a research paper on a idea Centerpoints: A Link Between Optimization and Convex Geometry"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a concept that generalizes several different notions of a \"centerpoint\" in the literature.  develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further,  show that algorithms based on centerpoints are \"best possible\" in a certain sense. Motivated by this,  establish several structural results about this concept and provide efficient algorithms for computing these points."}]