Untangling Lariats: Subgradient Following of Variationally Penalized Objectives

arXiv:2405.04710v1 Announce Type: new
Abstract: We describe a novel subgradient following apparatus for calculating the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence attains the minimum Bregman divergence to an input sequence with additive variational penalties in the general form of $\sum_i g_i(x_{i+1}-x_i)$. We derive, as special cases of our apparatus, known algorithms for the fused lasso and isotonic regression. Our approach also facilitates …

abstract arxiv cs.lg divergence math.oc minimum novel optimum seek type