Course description
Mathematical Optimization for Engineers
This course is useful to students of all engineering fields. The mathematical and computational concepts that you will learn here have application in machine learning, operations research, signal and image processing, control, robotics and design to name a few.
We will start with the standard unconstrained problems, linear problems and general nonlinear constrained problems. We will then move to more specialized topics including mixed-integer problems; global optimization for non-convex problems; optimal control problems; machine learning for optimization and optimization under uncertainty. Students will learn to implement and solve optimization problems in Python through the practical exercises.
Upcoming start dates
Who should attend?
Prerequisites:
You should have basic knowledge of linear algebra, vector calculus and ordinary differential equations. Familiarity with numerical computing is helpful but not required; programming tasks will be kept basic and simple. You will write simple Python scripts in Jupyter notebooks. We will provide some basic Python tutorials.
Training content
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
Unconstrained optimization
- Basics of iterative descent: step direction and step length
- Common algorithms like steepest descent, Newtons method and its variants and trust-region methods.
Linear optimization
- KKT conditions of optimality for constrained problems
- Simplex method
- Interior point methods
Nonlinear optimization
- Penalty, log-barrier and SQP methods
Mixed-integer optimization
- Branch and bound method for mixed-integer linear problems
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
Dynamic optimization
- Full discretization, single-shooting and multi-shooting methods
- Nonlinear model predictive control
Machine learning for optimization
- Mechanistic, data-driven and hybrid modelling>
- Basics of training machine learning models
- Optimization with machine learning embedded
Optimization under uncertainty
- Parametric optimization
- Two stage stochastic problems
- Robust optimization via semi-infinite problems
Course delivery details
This course is offered through RWTH Aachen University, a partner institute of EdX.
6-8 hours per week
Costs
- Verified Track -$99
- Audit Track - Free
Certification / Credits
What you'll learn
- 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
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