### **Technische Universität München, Zentrum Mathematik**

# **Case Studies in Nonlinear Optimization**

### **Combined Lecture and Project Work Course**

### **Dr. Florian Lindemann**

### **Summer Term 2017**

### Basic Concept- Projects - Registration/Preliminary Meeting

# Basic Concept

The description of this module**MA4513**can be found in TUMonline.

This course is a combination of a lecture part and an exercise part where an application example of nonlinear optimization is addressed by a team of three to five students. The lectures provide, on the one hand, mathematical theory and tools to solve the application examples and, on the other hand, cover topics as the organization of team work, the design of posters and the presentation of mathematical content to different target audiences.

The main part of this course are independent studies within a team of students. Consequently, team work and team organization are as important as profound mathematics, programming skills, modeling techniques or presentation skills.

# Projects

Here a short description of the projects: Project 1:**Optimization of a heat accumulator**

A heat accumulator (Wärmespeicher) is a tank containing water, which can be heated or can be taken out to heat a house. The question is when to supply heat to the tank. This depends on energy prices and energy losses. Here, a nonsmooth dynamic model comes into play. If, e.g., the upper water layers are warmer than the lower ones, the behaviour of the tank changes because of the occurring currents. In this project modelling aspects play a crucial role, based on an already existing, preliminary dynamic model. Different methods for time discretization and nonsmooth optimization can be used. Since the heat consumption is not known a priori, model predictive control could be a suitable tool also. This project is a cooperation with the Siemens AG. Project 2:

**Portfolio optimization with management and transaction costs**

One question in portfolio optimization is how to allocate wealth across assets to gain maximum profit while minimizing the associated risk, which is usually a contradiction. We want to compute risk averse portfolios and keep the necessary management and transaction costs low. Therefore, suitable risk measures (e.g., the conditional value-at-risk) and penalty terms are used in the objective function of the optimization problem. Hence, this problem is nonsmooth, but can be smoothed or reformulated as a smooth problem. Another important aspect is the question how to estimate the distribution of the asset returns. The results shall be tested with real market data. Project 3:

**Vision in robotics**

Optical sensors in robotics can be moved to different positions and every measurement is subject to uncertainty. Our partner Siemens AG has a simulation environment (in Ubuntu with a C++/Python interface) with different sensors and image recognition algorithms. In this project the measurements shall be planned optimally (optimal experimental design) and the appearing probability distributions shall be visualized and analyzed. Therefore, different aspects of visualization, modelling and testing of optimization algorithms, and also machine learning can be covered. This project is a cooperation with the Siemens AG. Project 4:

**Reconstruction of defective videos**

In videos, defective pixel values can appear in various forms such as scratches, unwanted logos, blurred or noisy parts. Therefore, one is interested in reconstruction or in improvement of damaged pixel areas in video frames. Mathematically, this problem can be formulated as a nonlinear optimization problem, where a "good" video reconstruction represents a minimum position. The aim of the project lies on experimenting with existing methods and algorithms on inpainting, deblurring and/or denoising as well as on trying new ideas/combinations beyond the existing ones. Project 5:

**Disparity determination in stereo vision**

In stereo vision, a traditional arrangement is the shot of a scene from two different point of views, similar to humans way of vision. The shot yields two similar images and one is interested in finding for each pixel in one image its corresponding pixel in the other image. This task is solved via the minimization of an objective function consisting of some similarity metric for pairs of image patches. For a pair of corresponding pixels, the magnitude of the (horizontal) shift of the pixel coordinates is called disparity and the set of disparities for all pixels is called disparity map. The disparity map can now be used for various applications such as distance calculation and depth perception, respectively (the Mars Exploration Rover used this concept for its navigation on the Mars surface!). In this project, standard algorithms and techniques for determining disparity maps shall be investigated and applied on datasets of standard benchmarks (Middlebury, KITTI, ...). Furthermore, the project is open on applying computed disparity maps on further tasks such as depth perception. This project will be in cooperation with Framos, a company with expertise in image processing.

# Registration

Registration for this course is mandatory and has to be done before the deadline:**Update: There are still free places left (not for the portfolio project).**

The registration is done by email to lindemannma.tum.de providing the following information:

- last name, first name.
- curriculum (of your master's studies).
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects.

(Example: (1) Project 3 (2) Project 1 (2) Project 4 (3) Project 2 (4) Project 5 - note that you can rate multiple projects with the same value.) - list of optimization related lectures that you have attended (for lectures from other faculties or universities, please give a short description of the topics covered so that we know about your expertise in the field).
- programming skills (programming languages and other programming related skills).
- persons you would like to work with as a team.

# Preliminary Meeting

The**preliminary meeting**was on

**February 6th, 2017 at 16:15 in room MI 03.08.011**(jointly with "Case Studies Discrete Optimization"). At this meeting we presented some information about the case studies courses in general, what to expect during the courses, this year's projects, important dates and the registration process. If you did not come to this meeting but would still like to take the course, some more information can be found in the slides below.

**Please note that a registration for this case study course is mandatory.**If you have any questions that are not answered here or at the preliminary meeting, please contact Florian Lindemann.

- Slightly shortened version of the slides: preliminary_meeting