Convex Cone Sparsification
Analysis
This paper introduces and analyzes a method for sparsifying sums of elements within a convex cone, generalizing spectral sparsification. It provides bounds on the sparsification function for specific classes of cones and explores implications for conic optimization. The work is significant because it extends existing sparsification techniques to a broader class of mathematical objects, potentially leading to more efficient algorithms for problems involving convex cones.
Key Takeaways
- •Introduces the sparsification function of a convex cone.
- •Generalizes spectral sparsification to a broader class of cones.
- •Provides bounds on the sparsification function for cones with certain barrier properties.
- •Explores the interaction of sparsification with convex geometric operations.
- •Discusses implications for conic optimization.
Reference
“The paper generalizes the linear-sized spectral sparsification theorem and provides bounds on the sparsification function for various convex cones.”