Module differentiable_optimization 

Differentiable optimization layers (OptNet-style LP/QP).

This module implements differentiable quadratic and linear programming layers that can be embedded in gradient-based training pipelines. The backward pass uses implicit differentiation of the KKT conditions to compute gradients of the optimal solution w.r.t. all problem parameters.

Submodules

• kkt_sensitivity: KKT bordered matrix assembly and adjoint-method sensitivity.
• qp_layer: ADMM-based QP layer with warm-start and active-set backward.
• lp_layer: Entropic LP layer and basis sensitivity analysis.
• perturbed_optimizer: Black-box differentiable combinatorial optimization.
• implicit_diff: Core implicit differentiation engine.
• combinatorial: SparseMAP, soft sort/rank (legacy entry points).
• diff_qp: Interior-point differentiable QP.
• diff_lp: Differentiable LP (active-set based).

References

• Amos & Kolter (2017). “OptNet: Differentiable Optimization as a Layer in Neural Networks.” ICML.
• Berthet et al. (2020). “Learning with Differentiable Perturbed Optimizers.” NeurIPS.
• Niculae & Blondel (2017). “A regularized framework for sparse and structured neural attention.” NeurIPS.

Re-exports

pub use combinatorial::diff_topk;

pub use combinatorial::soft_rank;

pub use combinatorial::soft_sort;

pub use combinatorial::sparsemap;

pub use combinatorial::sparsemap_gradient;

pub use combinatorial::PerturbedOptimizer as PerturbedOptimizerLegacy;

pub use combinatorial::PerturbedOptimizerConfig as PerturbedOptimizerLegacyConfig;

pub use combinatorial::SparsemapConfig;

pub use combinatorial::SparsemapResult;

pub use combinatorial::StructureType;

pub use diff_lp::DifferentiableLP;

pub use diff_qp::DifferentiableQP;

pub use kkt_sensitivity::kkt_matrix;

pub use kkt_sensitivity::kkt_sensitivity;

pub use kkt_sensitivity::mat_vec;

pub use kkt_sensitivity::outer_product;

pub use kkt_sensitivity::parametric_nlp_adjoint;

pub use kkt_sensitivity::regularize_q;

pub use kkt_sensitivity::sym_outer_product;

pub use kkt_sensitivity::KktGrad;

pub use kkt_sensitivity::KktSystem;

pub use kkt_sensitivity::NlpGrad;

pub use layer::OptNetLayer;

pub use layer::StandardOptNetLayer;

pub use lp_layer::lp_gradient;

pub use lp_layer::lp_perturbed;

pub use lp_layer::LpLayer;

pub use lp_layer::LpLayerConfig;

pub use lp_layer::LpSensitivity;

pub use perturbed_optimizer::PerturbedOptimizer;

pub use perturbed_optimizer::PerturbedOptimizerConfig;

pub use perturbed_optimizer::SparseMap;

pub use perturbed_optimizer::SparseMapConfig;

pub use qp_layer::QpLayer;

pub use qp_layer::QpLayerConfig;

pub use types::BackwardMode;

pub use types::DiffLPConfig;

pub use types::DiffLPResult;

pub use types::DiffOptGrad;

pub use types::DiffOptParams;

pub use types::DiffOptResult;

pub use types::DiffOptStatus;

pub use types::DiffQPConfig;

pub use types::DiffQPResult;

pub use types::ImplicitGradient;

pub use types::KKTSystem;

Modules

combinatorial

Differentiable Combinatorial Optimization

diff_lp

Differentiable Linear Programming.

diff_qp

Differentiable Quadratic Programming (OptNet-style).

implicit_diff

Core implicit differentiation engine for optimization layers.

kkt_sensitivity

KKT sensitivity analysis for differentiable optimization layers.

layer

OptNet layer abstraction for embedding differentiable optimization in neural network pipelines.

lp_layer

Differentiable LP layer via entropic regularization and basis sensitivity.

perturbed_optimizer

Differentiable combinatorial optimization via perturbed optimizers.

qp_layer

ADMM-based differentiable QP layer with warm-start and active-set backward.

types

Types for differentiable optimization (OptNet-style LP/QP layers).