T2: Minimization of functions and functionals

Format

Block course, 2 weeks

Contents

Basics of non-convex and non-linear optimisation; gradient-based algorithms; sequential quadratic programming (SQP); transcription methods; implementation and numerical issues; practical excercises.

Concepts

The participants will acquire a basic knowledge in the theory of non-convex and non- linear optimisation problems. This includes an overview of different problem classes (e.g., constrained, unconstrained, convex and non-convex) and fundamentals of first and second order optimality conditions. Furthermore the course will discuss gradient-based algorithms and efficient step-size control strategies.
The course will focus on sequential quadratic programming (SQP) techniques and implementation issues. This includes globalisation strategies (e.g., penalty-functions and filter-methods), regularisation and recovery strategies as well as sparsity considerations. The participants will learn how to use SQP methods to solve non-convex and non-linear optimisation problems by numerical excercises.
Regarding parameter identification problems in dynamic systems the course will give an intro- duction to transcription methods to convict infinite-dimensional to finite-dimensional optimisation problems.

Basic texts

• J. Nocedal, S. Wright. Numerical Optimization. Springer-Verlag New York, 2006.
• P. E. Gill, W. Murray, M. H. Wright Practical Optimization. Academic Press, 1981.