On a class of geodesically convex optimization problems solved via Euclidean MM methods. (arXiv:2206.11426v1 [math.OC])

Web: http://arxiv.org/abs/2206.11426

We study geodesically convex (g-convex) problems that can be written as a
difference of Euclidean convex functions. This structure arises in several
optimization problems in statistics and machine learning, e.g., for matrix
scaling, M-estimators for covariances, and Brascamp-Lieb inequalities. Our work
offers efficient algorithms that on the one hand exploit g-convexity to ensure
global optimality along with guarantees on iteration complexity. On the other
hand, the split structure permits us to develop Euclidean
Majorization-Minorization algorithms that help us bypass the …

arxiv math on optimization