| LEC # | TOPICS | KEY DATES |
|---|---|---|
1 | Introduction and Overview of the Course |
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2 | Overview of Nonlinear and Convex Optimization: i) Optimality Conditions ii) Newton’s Method iii) Interior Point Method iv) Dual Optimization v) Convex Optimization vi) Linear Program vii) Semidefinite Program | Problem set 1 out |
3 | Nonlinear Optimization Using the Theory of Nonnegative Polynomials Sum-of-Squares Formulation (SOS) | Problem set 1 due Problem set 2 out |
4 | Nonlinear Optimization Using the Theory of Measure and Moments | Problem set 2 due Problem set 3 out |
5 | Duality i) Duality of Moments and Polynomials ii) Duality of Measures and Continuous Functions | Problem set 3 due Problem set 4 out |
6 | Modified Sum-of-Squares Optimization i) Spars Sum-of-Squares Optimization (SOS) ii) Bounded Degree Sum-of-Squares Optimization (BSOS) iii) (Scaled) Diagonally Dominant Sum-of-Squares Optimization (SDSOS, DSOS) | Problem set 4 due Problem set 5 out |
7 | Chance Optimization and Chance-Constrained Optimization i) Measure and Moments Formulation ii) Sum-of-Squares Formulation | Problem set 5 due |
8 | Part 1: Robust Optimization Using Sum-of-Squares Optimization Part 2: Distributionally Robust Chance-Constrained Optimization | Problem set 6 out |
9 | Algorithms for Large-Scale Semidefinite Programs (Guest Lecture) | Problem set 6 due Problem set 7 out |
10 | Safety Verification of Probabilistic Systems i) Risk Estimation ii) Probabilistic Uncertainty Propagation iii) Uncertainty Set Construction iv) Forward-Reachable Sets | Problem set 7 due |
11 | Risk Aware Planning and Control i) Risk-Bounded Trajectory Planning ii) Risk Aware Nonlinear Control iii) Flow-Tube–Based Control iv) Backward-Reachable Sets |
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12 | Dynamical Systems with Gaussian Uncertainties i) Chance-Constrained Control ii) Safety Verification iii) Distributionally Robust Chance Constraints |
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13 | Occupation Measure-Based Analysis and Control i) Safety Verification ii) Region-of-Attraction Set iii) Optimal Control |
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14 | Sum-of-Squares Optimization for Uncertain Nonlinear Systems i) Lyapunov-Based Stability and Region-of-Attraction Set ii) Barrier-Function–Based Safety Verification iii) Robust Control |
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15 | Final Project Presentation |
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