Module Number ML4303 
Module Title Convex and Nonconvex Optimization 
Lecture Type(s) Lecture, Tutorial 

ECTS  9  
Work load  Contact time  Self study 
Workload:
270 h Class time:
90 h / 6 SWS Self study:
180 h 

Duration  1 Semester  
Frequency  Irregular  
Language of instruction  English  
Type of Exam  Written exam (in case of a small number of participants: oral tests) 

Content  Convex optimization problems arise quite naturally in many application areas like signal processing, machine learning, image processing, communication and networks and finance etc. The course will give an introduction into convex analysis, the theory of convex optimization such as duality theory, algorithms for solving convex optimization problems such as interior point methods but also the basic methods in general nonlinear unconstrained minimization, and recent firstorder methods in nonsmooth convex optimization. We will also cover related nonconvex problems such as d.c. (difference of convex) programming, biconvex optimization problems and hard combinatorial problems and their relaxations into convex problems. While the emphasis is given on mathematical and algorithmic foundations, several example applications together with their modeling as optimization problems will be discussed. The course requires a good background in linear algebra and multivariate calculus, but no prior knowledge in optimization is required. 

Objectives  Students learn the foundations of convex analysis and how to formulate and transform optimization problems. After the lecture they know a variety of methods for solving convex and nonconvex optimization problems and have guidelines which method to choose for which problem. 

Allocation of credits / grading 
Type of Class
Status
SWS
Credits
Type of Exam
Exam duration
Evaluation
Calculation
of Module (%)
Lecture
V
o
4
6.0
wt
90
100
Tutorial
Ü
o
2
3.0


Prerequisite for participation  There are no specific prerequisites.  
Lecturer / Other  Hein  
Literature  The lecture does not follow a specific book. The literature for this lecture will be provided at the beginning of the semester. 

Last offered  Sommersemester 2022  
Planned for  currently not planned  
Assigned Study Areas  INFOINFO, INFOTHEO, MEDIAPPL, MEDIINFO, MLCS, MLDIV 