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6.7220J | Spring 2025 | Graduate

# Nonlinear Optimization

In addition to the PDF versions of the lecture notes below, the notes are available in an HTML version on the instructor’s website.

Lecture 1: Introduction (PDF) | (HTML)

Lecture 2: First-Order Optimality Conditions (PDF) | (HTML)

Lecture 3: More on Normal Cones, and a First Taste of Duality (PDF) | (HTML)

Lecture 4: The Special Case of Convex Functions (PDF) | (HTML)

Lecture 5: The Driver of Duality: Separation (PDF) | (HTML)

Lecture 6: Separation as a Proof System (PDF) | (HTML)

Lecture 7: Lagrange Multipliers and KKT Conditions (PDF) | (HTML)

Lecture 8: Lagrangian Duality (PDF) | (HTML)

Lecture 9: Conic Optimization (PDF) | (HTML)

Lecture 10: Polynomial Optimization (PDF) | (HTML)

Lecture 11: Polarity and Oracle Equivalence (PDF) | (HTML)

Lecture 12: Gradient Descent and Descent Lemmas (PDF) | (HTML)

Lecture 13: Acceleration and Momentum (PDF) | (HTML)

Lecture 14: Projected Gradient Descent and Mirror Descent (PDF) | (HTML)

Lecture 15: Stochastic Gradient Descent (PDF) | (HTML)

Lecture 16: Distributed Optimization and ADMM (PDF) | (HTML)

Lecture 17: Hessians, Preconditioning, and Newton’s Method (PDF) | (HTML)

Lecture 18: Adaptive Preconditioning: AdaGrad and ADAM (PDF) | (HTML)

Lecture 19: Self-Concordant Functions (PDF) | (HTML)

Lecture 20: Central Path and Interior-Point Methods (PDF) | (HTML)

Lecture 21: Bayesian Optimization (PDF)

## Course Info

##### Instructor

- Prof. Gabriele Farina

##### Departments

- Electrical Engineering and Computer Science
- Sloan School of Management

##### As Taught In

Spring 2025

##### Level

Graduate

##### Topics

- Engineering
  - Computer Science
    - Theory of Computation
  - Systems Engineering
    - Systems Optimization
- Mathematics
  - Applied Mathematics

##### Learning Resource Types

grading Exam Solutions
grading Exams
notes Lecture Notes
assignment_turned_in Problem Set Solutions
assignment Problem Sets
grading Supplemental Exam Materials

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