• Mathematical definitions of objective function, degrees of freedom, constraints and optimal solution
• Mathematical as well as intuitive understanding of optimality conditions
• Different optimization formulations (unconstrained v/s constrained; linear v/s nonlinear; mixed-integer v/s continuous; time-continuous or dynamic; optimization under uncertainty)
• Fundamentals of the solution methods for each these formulations
• Optimization with machine learning embedded
• Hands-on training in implementing and solving optimization problems in Python, as exercises

Week 1: Introduction and math review

• Mathematical definitions of objective function, degrees of freedom, constraints and optimal solution with real-world examples
• Review of some mathematical basics needed to take us through the course

Week 2: Unconstrained optimization

• Basics of iterative descent: step direction and step length
• Common algorithms like steepest descent, Newton’s method and its variants and trust-region methods.

Week 3: Linear optimization

• KKT conditions of optimality for constrained problems
• Simplex method
• Interior point methods

Week 4: Nonlinear optimization

• Penalty, log-barrier and SQP methods

Mixed-integer optimization

• Branch and bound method for mixed-integer linear problems

Week 5: Global optimization

• Branch and bound method for nonlinear non-convex problems
• Constructing relaxations
• Different formulations and their numerical performance
• Stochastic methods, genetic algorithm and derivative free methods

Week 6: Dynamic optimization

• Full discretization, single-shooting and multi-shooting methods
• Nonlinear model predictive control

Week 7: Machine learning for optimization

• Mechanistic, data-driven and hybrid modelling
• Basics of training machine learning models
• Optimization with machine learning embedded

Week 8: Optimization under uncertainty

• Parametric optimization
• Two stage stochastic problems
• Robust optimization via semi-infinite problems