Mathematical Optimization

2018-2019

Course Objective

After completing this course:
1. You can formulate a problem as an optimization model in a correct and
efficient way.
2. You understand when you need to use discrete decision variables and
the impact of those in the effort required to solve problems.
3. You can prove that a given model is convex, and you can characterize
the optimal solutions and formulate the equivalent dual model.
4. You can reformulate most of the convex models into Second Order Conic
Optimization models that can be efficiently solved even if the instance
is very large.
5. You are able to translate robust requirements, that need an infinite
number of constraints, into equivalent but finite problems that you can
solve.
6. You can solve small problems of all the types studied on paper and
problems of practical size on the computer.

Course Content

Mathematical optimization is among the most important instruments of
Prescriptive Analytics and is used to take decisions based on
quantitative arguments. Our daily life is full of examples of the
importance of optimization: for most trucks on the road, origin,
destination, load and even its route have been determined by an
optimization algorithm, leading to increased efficiency and lower
environmental impact. The battery life of your phone would be
significantly shorter if the chip lay-out was not optimized.
Side-effects of radiotherapy would be more severe if cancer treatment
was not personalized with state-of-the-art optimization algorithms.

This course will make you familiar with translating practical problems
into optimization models, and with solving those models. Despite the
goal of teaching you how to solve problems, this course teaches you the
fundamental results from the mathematics of optimization, including
optimality conditions, duality and robust optimization.

The course covers linear optimization as well as its generalizations
(conic and convex optimization). We will briefly consider optimization
under uncertainty. Optimization models will be implemented and solved
using mostly software that is freely available to all (e.g. Python) and
occasionally software that is free for academics but requires purchasing
for commercial use.

Teaching Methods

The course consists of the following contact moments:
Lectures in 2 blocks of 1:45 per week.
Tutorials in 1 block of 1:45 per week.
Computer lab in 1 block of 1:45 per week.
Presence and active participation is expected during all the above.

Method of Assessment

Exam (60%)
Practical assignments (40%)
The practical assignments cannot be repeated. To pass:
- The grade for the exam needs to be 5.0 or higher,
- The weighted average needs to be 5.5 or higher.

Entry Requirements

A first course in Operations Research and Linear Algebra.

Literature

Convex optimization, Boyd & Vandenberghe (pdf freely available)
AIMMS optimization modeling (pdf freely available)
Nonlinear Optimization by E. de Klerk, C. Roos, and T. Terlaky (pdf
freely available)
Slides

Target Audience

Students of Business Analytics, Econometric and Operations Research, or
other master programs with a strong quantitative accent interested in
Mathematical Optimization theory and practice.

This course is not intended for students who followed the course
Mathematical Optimization in their minor due to considerable overlap.

Additional Information

Students that follow LNMB courses may find that Mathematical
Optimization intersects Continuous Optimization, Discrete Optimization
and Advanced Linear Programming. It, does, however not fully overlap any
of those and distinguishes itself by covering Second Order Conic
Optimization, Robust Optimization and by teaching how to model and solve
problems in the computer using Python.

Explanation Canvas

The slides, assignments and additional information will be made
available via Canvas.

Recommended background knowledge

Besides introduction to Operations Research and Linear Algebra you
should be familiar with at least one programming language, preferably
Python.

General Information

Course Code XM_0051
Credits 6 EC
Period P2
Course Level 400
Language of Tuition English
Faculty Faculty of Science
Course Coordinator prof. dr. J.A. Dos Santos Gromicho
Examiner prof. dr. J.A. Dos Santos Gromicho
Teaching Staff drs. B.G. Zweers
prof. dr. J.A. Dos Santos Gromicho

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture, Computer lab
Target audiences

This course is also available as: