Summer school on Aspects of Optimization

Continuous Optimization
Ekaterina Kostina
Universität Heidelberg, Germany

Mathematical and computational optimization is a highly topical research area of enormous relevance in all areas of advanced science and engineering that rely on mathematical models and computational simulation. This course is devoted to continuous optimization, one of the sub-areas of mathematical optimization that deals with optimization problems with continuous variables. The aim of the course is to introduce fundamentals of nonlinear optimization theory and methods. We will start with optimality conditions for nonlinear unconstrained and constrained optimization. Then we will continue with basic algorithms for unconstrained optimization including steepest descent, Newton’ method and quasi-Newton methods, and strategies ensuring convergence such as line-search and trust-region methods. We will discuss implementation details and convergence properties of the methods. Finally, we will give an overview of practical optimization algorithms for constrained optimization including Sequential Quadratic Programming (SQP) and interior-point methods.

Slides / Exercises