 Graphical-Lasso Karush-Kuhn-Tucker conditions

ID: graphical-lasso-karush-kuhn-tucker-conditions

Codex  0 Created 2026-09-24 Updated 2026-10-06

For objective

- lo g det Ω + Tr (S Ω) + λ ∥ Ω ∥_{1, entry}

, the KKT conditions are

- Ω^{- 1} + S + λ Z = 0

with

Z_{ij} \in \partial ∣ Ω_{ij} ∣

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