Numerical optimisation

Unit Coordinator: Kevin Sturm
Programme: Erasmus Mundus
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

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