Complexity and Runtime Behavior of Solvers for Obstacle Problems
Program Director UROP
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- Project Offer-Number:
- UROP International, UROP Network
- Computational Engineering Science
- Organisation unit:
- Aachen Institute for Advanced Study in Computational Engineering Science (AICES) RWTH Aachen Univers
- Language Skills:
- English / (German can be practiced with the supervisor).
- Computer Skills:
- Basic Programming skills (MATLAB).
Constrained minimization problems are mathematical problems involving inequalities, which occur in a wide variety of applications, such as solid and fluid mechanics, and finance. One of the simplest examples of a constrained minimization problem is the obstacle problem. Consider, for example, a thin membrane with a fixed boundary and on which a downward force is applied. If there is no obstacle below the membrane, the problem is just linear and easy to solve. But if there is an obstacle placed close to the membrane, the problem is considerably more difficult. In the latter, we would need to distinguish between two regions: (i) the region of contact and (ii) the region of unconstrained displacement. There are many different methods available for solving such constrained minimization problems. Some are trying to determine the above-mentioned regions. Some try to solve a modified form of the problem, while others try to solve the constrained minimization problem directly.
In this project, we would like to compare the performance of different methods for solving such problems. In particular, we would like to investigate the interior point method, penalty method, primal-dual active set method and projection based methods. Your tasks will be to: -familiarize yourself with constrained minimization problems; -understand the solution process using the interior point method; -implement solution methods in MATLAB and compare their runtime behavior in best and worst case scenarios.
The student should have basic familiarity with MATLAB. Basic knowledge of Numerical Analysis would be helpful.