NLP Tutorial Series

A series of 15 Jupyter notebooks taking you from "beginner in nonlinear programming" to understanding every component of ripopt — written in Python (numpy, scipy, matplotlib), with each notebook connecting directly to ripopt's source code.

All notebooks are in tutorials/ in the repository.

Module 1: NLP Foundations

#	Notebook	Key concepts
01	Introduction to Nonlinear Programming	Problem formulation, feasibility vs optimality, HS071
02	Unconstrained Optimization	Gradient descent, Newton's method, Armijo/Wolfe line search, L-BFGS
03	KKT Conditions	Lagrangian, complementarity, geometric interpretation, LICQ

Module 2: Classical Constrained Methods

#	Notebook	Key concepts
04	Penalty Methods and Augmented Lagrangian	Quadratic penalty, ill-conditioning, Method of Multipliers
05	Sequential Quadratic Programming	QP subproblem, active set, BFGS update, L1 merit function

Module 3: Barrier Methods

#	Notebook	Key concepts
06	The Logarithmic Barrier Method	Log barrier, central path, barrier parameter sequence
07	Primal-Dual Interior Point Method	Perturbed KKT, Newton step derivation, fraction-to-boundary, complete IPM

Module 4: Linear Algebra at the Core

#	Notebook	Key concepts
08	The KKT (Saddle-Point) Matrix	KKT structure, Sylvester's Law of Inertia, condensed KKT
09	LDL^T and Bunch-Kaufman Pivoting	Symmetric Gaussian elimination, BK pivoting, inertia from D
10	Inertia Correction and Regularization	δ_w and δ_c perturbations, correction loop, iterative refinement

#	Notebook	Key concepts
11	Filter Line Search	Filter concept, acceptance criteria, switching condition, SOC
12	Convergence Criteria and Scaling	Three KKT residuals, s_d/s_c scaling, NLP scaling

Module 6: Robustness

#	Notebook	Key concepts
13	The Restoration Phase	Gauss-Newton restoration, NLP restoration subproblem, recovery strategies
14	Mehrotra Predictor-Corrector	Affine-scaling predictor, adaptive centering σ = (μ_aff/μ)³, Gondzio corrections

Module 7: ripopt in Practice

#	Notebook	Key concepts
15	ripopt in Practice	NlpProblem interface, fallback cascade, sensitivity analysis, benchmarking

Running the notebooks

git clone https://github.com/jkitchin/ripopt.git
cd ripopt/tutorials
pip install numpy scipy matplotlib jupyter
jupyter lab

Each notebook is self-contained. No Rust installation required for notebooks 01–14. Notebook 15 describes the Rust interface with Python equivalents for all concepts.

ripopt source pointers

Each notebook ends with a "Connection to ripopt" section. The key mappings:

Topic	Notebook	ripopt source
KKT assembly	08	`src/kkt.rs` — `assemble_kkt()`
Bunch-Kaufman LDL^T	09	`src/linear_solver/dense.rs` — `DenseLdl`
Inertia correction	10	`src/kkt.rs` — `factor_with_inertia_correction()`
Filter line search	11	`src/filter.rs` — `check_acceptability()`
Convergence	12	`src/convergence.rs` — `check_convergence()`
Restoration	13	`src/restoration.rs`, `src/restoration_nlp.rs`
Mehrotra PC	14	`src/ipm.rs` — main loop
Problem interface	15	`src/problem.rs` — `NlpProblem` trait