Centerpoints: A Link Between Optimization and Convex Geometry
نویسندگان
چکیده
We introduce a concept that generalizes several different notions of a “centerpoint” in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are “best possible” in a certain sense. Motivated by this, we establish structural results about this concept and provide efficient algorithms for computing these points. Our main motivation is to understand the complexity of oracle-based convex mixed-integer optimization.
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