Hands On Training

Mathematical Optimization for Engineers

RWTH Aachen University

via

edX

Course Features

Duration

8 weeks

Delivery Method

Online

Available on

Limited Access

Accessibility

Mobile, Desktop, Laptop

Language

English

Subtitles

English

Level

Intermediate

Effort

8 hours per week

Teaching Type

Self Paced

Course Description

Today, for almost every product on the market and almost every service offered, some form of optimization has played a role in their design.

However, optimization is not a button-press technology. To apply it successfully, one needs expertise in formulating the problem, selecting and tuning the solution algorithm and finally, checking the results. We have designed this course to make you such an expert.

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.

Course Overview

International Faculty

Post Course Interactions

Instructor-Moderated Discussions

Skills You Will Gain

Prerequisites/Requirements

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.

What You Will 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

Course Content

Expand all sections

Module 1: Introduction and math review

Module 2: Unconstrained optimization

Module 3: Linear optimization

Module 4: Nonlinear optimization

Course Instructors

Univ.-Prof. Alexander Mitsos

Director of Process Systems Engineering (AVT.SVT) Laboratory at RWTH Aachen University

Alexander Mitsos is an expert researcher in optimization theory and applications. He serves as the director of Process Systems Engineering (AVT.SVT) laboratory at RWTH Aachen University and the Energ...

Johannes M. M. Faust

Doctoral Student in AVT.SVT at RWTH Aachen University

Johannes Faust is a doctoral student in AVT.SVT. He received his Master’s degree in automation and his Bachelor’s in Mechanical Engineering with specialization in Chemical Engineering from RWTH Aache...

Ashutosh Manchanda

Doctoral Student in AVT.SVT at RWTH Aachen University

Ashutosh Manchanda is a doctoral student in AVT.SVT. He received his Master’s degree in Simulation Sciences from RWTH Aachen University and his Bachelor’s in Mechanical Engineering from IIT Dhanbad. ...