- ECTS Credits: 4
- Year: 2
- Campus: Silesian University of Technology
- ECTS Credits: 4
- Year: 2
- Campus: Brno University of Technology
- Language: English
- Code: DT0371
- Unit Coordinator: Kevin Sturm, Phillip Baumann
- ECTS Credits: 6
- Semester: 2
- Year: 1
- Campus: Vienna University of Technology
- Language: English
- Aims:
To understand, analyze, formulate and graphically or mathematically solve basic static and dynamic optimization problems. Students will know about the theory, the mathematically principles and various methods for an exact or iterative solution of optimization problems.
They can moreover differentiate between unconstrained and constrained optimization problems and they can select and apply the specifically appropriate solution methods.
- Content:
- Fundamentals of optimization: existence of minima and maxima, gradient, Hessian, convexity, convergence
- Unconstrained static optimization: optimality conditions, computer-aided optimization, line search methods, choice of the step length, principle of nested intervals, Armijo condition, Wolfe condition, gradient method, Newton method, conjugate gradient method, Quasi-Newton method, Gauss-Newton-method, trust region method, Nelder-Mead method
- Static optimization with constraints: equality and inequality constraints, sensitivity considerations, active set method, gradient projection method, reduced gradient method, penalty and barrier functions, sequential quadratic programming (SQP), local SQP, globalization of SQP
- Pre-requisites:
- Analysis,
- Linear algebra,
- Numerical mathematics,
- Differential equations.
- Reading list:
- lecture notes,
- J. Macki und A. Strauss: Introduction to Optimal Control Theory. New York, Springer, 1982.
- Jorge Nocedal, Stephen J. Wright: Numerical Optimization, Springer 2006
- Unit Coordinator: Josef Weinbub
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: Vienna University of Technology
- Language: English
- Aims:
Students will be able to select and apply fundamental methods of scientific computing and to judge the challenges regarding computing time and implementation effort.
Furthermore, the students have solution skills for inter-disciplinary problems, are able to evaluate and analyze computational approaches, and are able to scientifically formulate and extensively analyze compute-intensive problems as well as develop appropriate approaches.
- Content:
- Computer Architectures
- Serial Optimization
- Numerical Derivatives and Integrals
- Finite Difference Discretization
- Numerical Linear Algebra
- Random Number Generation and Monte Carlo Methods
- Shared Memory Parallel Computing
- Algorithmic Complexity and Data Structures
- Mesh Generation and Visualization
- Software Engineering Principles for Scientific Computing
- Pre-requisites:
Numerical mathematics, scientific programing.
- Reading list:
Lecture notes
