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6.7220J | Spring 2025 | Graduate

# Nonlinear Optimization

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Lecture 1: Introduction
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Lecture 2: First-Order Optimality Conditions
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Lecture 3: More on Normal Cones, and a First Taste of Duality
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Lecture 4: The Special Case of Convex Functions
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Lecture 5: The Driver of Duality: Separation
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Lecture 6: Separation as a Proof System
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Lecture 7: Lagrange Multipliers and KKT Conditions
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Lecture 8: Langrangian Duality
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Lecture 9: Conic Optimization
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Lecture 10: Polynomial Optimization
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Lecture 11: Polarity and Oracle Equivalence
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Lecture 12: Gradient Descent and Descent Lemmas
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Lecture 13: Acceleration and Momentum
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Lecture 14: Projected Gradient Descent and Mirror Descent
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Lecture 15: Stochastic Gradient Descent
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Lecture 16: Distributed Optimization and ADMM
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Lecture 17: Hessians, Preconditioning, and Newton's Method
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Lecture 18: Adaptive Preconditioning: AdaGrad and ADAM
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Lecture 19: Self-Concordant Functions
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Lecture 20: Central Path and Interior-Point Methods
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Lecture 21: Bayesian Optimization

## 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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