LEC #  TOPICS  KEY DATES 

1 
Introduction and Overview of the Course 

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 SumofSquares 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 SumofSquares Optimization i) Spars SumofSquares Optimization (SOS) ii) Bounded Degree SumofSquares Optimization (BSOS) iii) (Scaled) Diagonally Dominant SumofSquares Optimization (SDSOS, DSOS) 
Problem set 4 due Problem set 5 out 
7 
Chance Optimization and ChanceConstrained Optimization i) Measure and Moments Formulation ii) SumofSquares Formulation 
Problem set 5 due 
8 
Part 1: Robust Optimization Using SumofSquares Optimization Part 2: Distributionally Robust ChanceConstrained Optimization 
Problem set 6 out 
9 
Algorithms for LargeScale 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) ForwardReachable Sets 
Problem set 7 due 
11 
Risk Aware Planning and Control i) RiskBounded Trajectory Planning ii) Risk Aware Nonlinear Control iii) FlowTube–Based Control iv) BackwardReachable Sets 

12 
Dynamical Systems with Gaussian Uncertainties i) ChanceConstrained Control ii) Safety Verification iii) Distributionally Robust Chance Constraints 

13 
Occupation MeasureBased Analysis and Control i) Safety Verification ii) RegionofAttraction Set iii) Optimal Control 

14 
SumofSquares Optimization for Uncertain Nonlinear Systems i) LyapunovBased Stability and RegionofAttraction Set ii) BarrierFunction–Based Safety Verification iii) Robust Control 

15 
Final Project Presentation 
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2019
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