A graph decomposition framework is introduced that uses the network to design the method, not merely execute it, and it jointly determines how agreement is imposed, which variables are optimized jointly (blocks), and which connected subgraphs host the agents solving each block.
We study the minimization of sums of smooth strongly convex functions over undirected graphs, with each function held by one agent and communication restricted to neighbors in the graph. Existing decentralized methods, whether based on gossip or on routing over spanning trees, typically use the network to mix or aggreg...
Sequence convergence to a boundary Karush--Kuhn--Tucker (KKT) point has long remained unclear for nonconvex mirror descent with Legendre kernels. The difficulty arises from the blow-up of the gradient of the Legendre kernel at the boundary. Recent work~\cite{dingtoh2026nonkkt} shows that mirror descent can accumulate a...
For mirror descent generated by a Legendre kernel, perhaps one of the most basic question in optimization is this: must every accumulation point of a bounded mirror descent sequence be Karush--Kuhn--Tucker (KKT) stationary under proper stepsizes? We show that the answer is no. A longstanding obstacle to resolving this...
Kuangyu Ding, Kim-Chuan Toh· 1 citation
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
