Dual Lagrangian Learning for Conic Optimization

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology that combines conic duality theory with the represen- tation power of ML models. DLL leverages conic duality to provide dual-feasible solutions, and therefore valid Lagrangian dual bounds, for para- metric linear and nonlinear conic optimization problems. The paper introduces differentiable conic projection layers, a systematic dual com- pletion procedure, and a self-supervised learning framework. The effectiveness of DLL is demon- strated on linear and nonlinear parametric opti- mization problems …

cs.lg differentiable linear math.oc methodology ml models optimization paper power projection solutions theory