Multiplicative updates for symmetric-cone factorizations
Yong Sheng Soh, Antonios Varvitsiotis

TL;DR
This paper introduces the symmetric-cone multiplicative update (SCMU) algorithm for computing cone factorizations over symmetric cones, unifying various optimization problems like LPs, SOCPs, and SDP, with theoretical guarantees.
Contribution
The paper develops and analyzes the SCMU algorithm for symmetric-cone factorizations, extending multiplicative updates to a broad class of cones with convergence properties.
Findings
The squared loss is non-decreasing along SCMU trajectories.
Special case recovers Lee and Seung's NMF algorithm.
The method applies to LPs, SOCPs, and SDPs.
Abstract
Given a matrix with non-negative entries, the cone factorization problem over a cone concerns computing and belonging to its dual so that for all . Cone factorizations are fundamental to mathematical optimization as they allow us to express convex bodies as feasible regions of linear conic programs. In this paper, we introduce and analyze the symmetric-cone multiplicative update (SCMU) algorithm for computing cone factorizations when is symmetric; i.e., it is self-dual and homogeneous. Symmetric cones are of central interest in mathematical optimization as they provide a common language for studying linear optimization over the nonnegative orthant (linear…
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Mathematical Inequalities and Applications
