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This course blends optimization theory and computation and its teachings can be applied to modern data analytics, economics, and engineering. Organized across four modules, it takes learners through basic concepts, models, and algorithms in linear optimization, convex optimization, and integer optimization.
The first module of the course is a general overview of key concepts in linear algebra, calculus, and optimization. The second module of the course is on linear optimization, covering modeling techniques with many applications, basic polyhedral theory, simplex method, and duality theory. The third module is on convex conic optimization, which is a significant generalization of linear optimization. The fourth and final module focuses on integer optimization, which augments the previously covered optimization models with the flexibility of integer decision variables.
Overview
Syllabus
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Week 1
- Module 1: Introduction
- Module 2: Illustration of the Optimization Problems
Week 2
- Module 3: Review of Mathematical Concepts
- Module 4: Convexity
Week 3
- Module 5: Outcomes of Optimization
- Module 6: Optimality Certificates
Week 4
- Module 7: Unconstrained Optimization: Derivate Based
- Module 8: Unconstrained Optimization: Derivative Free
Week 5
- Module 9: Linear Optimization Modeling – Network Flow Problems
- Module 10: Linear Optimization Modeling – Electricity Markets
Week 6
- Module 11: Linear Optimization Modeling – Decision-Making Under Uncertainty
- Module 12: Linear Optimization Modeling – Handling Nonlinearity
Week 7
- Module 13: Geometric Aspects of Linear Optimization
- Module 14: Algebraic Aspect of Linear Optimization
Midterm
Week 8- Module 15: Simplex Method in a Nutshell
- Module 16: Further Development of Simplex Method
Week 9
- Module 17: Linear Programming Duality
- Module 18: Robust Optimization
Week 10
- Module 19: Nonlinear Optimization Modeling – Approximation and Fitting
- Module 20: Nonlinear Optimization Modeling – Statistical Estimation
Week 11
- Module 21: Convex Conic Programming – Introduction
- Module 22: Second-Order Conic Programming – Examples
Week 12
- Module 23: Second-Order Conic Programming – Advanced Modeling
- Module 24: Semi-definite Programming – Advanced Modeling
Week 13
- Module 25: Discrete Optimization: Introduction
- Module 26: Discrete Optimization: Modeling with binary variables - 1
Week 14
- Module 27: Discrete Optimization: Modeling with binary variables – 2
- Module 28: Discrete Optimization: Modeling exercises
Week 15
- Module 29: Discrete Optimization: Linear programming relaxation
- Module 30: Discrete Optimization: Solution methods
