# LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization Source: [LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization]() Collection index: [llms.txt]() Data updated: 2026-06-10T05:01:35.776Z Authors: Binh Nguyen, Trinh Tran, Truong X. Nghiem Published: 2026-06-08T03:44:20.000Z ## Abstract We propose LEAF, a learning-enabled ADMM framework for accelerated convex optimization. The key idea is to approximate the Moreau envelope of the objective function using an Input Convex Neural Network (ICNN), resulting in a learned model that preserves convexity and smoothness. This leads to the proposed Moreau Envelope Learning ADMM (MEL-ADMM) and its splitting variant sMEL-ADMM. Unlike existing approaches that learn high-dimensional operators directly, LEAF learns a scalar-valued Moreau envelope, significantly reducing model complexity and improving data efficiency. The framework accommodates a broad class of convex problems with smooth and non-smooth objectives. By embedding convexity explicitly through the ICNN architecture, the proposed approach maintains high approximation accuracy while preserving key structural properties of the optimization problem. Both MEL-ADMM and sMEL-ADMM are developed with theoretical guarantees of convergence and feasibility under the learned model. Rigorous analysis shows that the proposed methods achieve convergence rates comparable to classical ADMM while reducing per-iteration computational cost. Numerical experiments demonstrate up to an order-of-magnitude speedup over state-of-the-art solvers while maintaining low optimality gaps ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Minimum Volume Enclosing Ellipsoid optimization on Example 3 MVEE 1000 randomized instances](): Minimum Volume Enclosing Ellipsoid optimization; Example 3 MVEE 1000 randomized instances; Average Solving Time (ms): 0.18. - [Energy Management Optimization on Microgrid Energy Management N=96](): Energy Management Optimization; Microgrid Energy Management N=96; Computation Time (ms): 0.5. - [Energy Management Optimization on Microgrid Energy Management (N=192)](): Energy Management Optimization; Microgrid Energy Management (N=192); Computation time (ms): 0.7. ## Original sources and implementation [Original paper]() [PDF]()