Scaled relative graphs are extended to normed spaces via directional pairings from regular pairings, yielding geometric containment tests for contraction and monotonicity.
Beck,First-Order Methods in Optimization
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The paper introduces a non-negative DAG learning formulation solved via method of multipliers, with proofs that the true DAG is the unique global minimizer and only acyclic KKT point in the population regime.
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Scaled Relative Graphs in Normed Spaces
Scaled relative graphs are extended to normed spaces via directional pairings from regular pairings, yielding geometric containment tests for contraction and monotonicity.
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Exploiting Non-Negativity in DAG Structure Learning
The paper introduces a non-negative DAG learning formulation solved via method of multipliers, with proofs that the true DAG is the unique global minimizer and only acyclic KKT point in the population regime.