Bridging the Gap

Bridging The Gap: Knowledge Workshop 1

Workshop 1: Aspects of Mathematical optimization - 19th June 2008, 9 AM to 2 PM, European Research Institute

Workshop presentations

  • Michal Kocvara: Current trends in nonlinear optimisation PDF
  • Matthias Gerdts: Optimal Control Problems and Applications in Egineering PDF
  • Sandor Nemeth: Equilibrium systems PDF

Synopsis

Workshop one will explore the methods of mathematical optimization, and their applications in different areas

This event is particulary aimed at anyone with an interest in introducing optimization techniques into their work.

Program

9:00 AM Tea and Coffee
9:30 AM Current trends in nonlinear optimisation

In the first part of the talk I will give a brief overview of current trends in nonlinear optimisation with the emphasis on algorithms and numerical solution. I will try to show the capabilities and limitations of nonlinear optimisation codes in various areas.

In the second part I will concentrate on one particular area of optimisation, semidefinite programming, and show some of the many application areas of this new emerging discipline.

Prof. Michal Kocvara
10:15 AM Optimal Control Problems and Applications in Egineering

The talk discusses numerical methods for optimal control problems with ordinary differential equations and shows how they can be extended to mixed-integer optimal control problems and real-time optimal control problems.

The first part of the talk discusses different approaches to the numerical solution of optimal control problems: the direct discretization approach and a semismooth Newton method. The direct discretization approach transforms the optimal control problem into a possibly large-scale and sparse nonlinear program which is solved by an SQP method and turns out to be very powerful in practice. The semismooth Newton method is a variant of Newton's method for nonlinear equations and aims at satisfying first order necessary optimality conditions of the optimal control problem using a nonlinear complementarity function. The same method can also be used in the simulation of mechanical multibody systems with contact conditions.

The second part of the talk briefly discusses extensions toward real-time optimization using sensitivity analysis and mixed-integer optimal control problems using a suitable time transformation.

Finally numerical results for selected applications from aerospace engineering PDE control and vehicle simulation will be presented.

Dr. Matthias Gerdts
11:00 AM Coffee Break (Atrium)
11:30 AM Equilibrium systems
Equilibrium is ''everywhere'': in economics, physics, engineering, chemistry, biology etc. From the mathematical modelling point of view equilibrium can be described by different types of systems such as fixed point theorems, optimisation problems, variational inequalities, complementarity problems etc. Equilibrium systems can be studied from several points of view: existence of solutions; existence of nontrivial solutions; number of solutions; properties of the solution set; and the numerical approximation of solutions. After a short description of what constitutes a mathematical equilibrium system in general, particular equilibrium problems will be considered and analysed.
Dr. Sandor Nemeth
12:15 PM Question and Answer session
1:00 PM Lunch (Atrium)

Location

The workshop will be held in the atrium and conference room of the European Research Institute building, Pritchatts Road (Building G3 in the green zone).