The Johann Radon Institute for Computational and Applied Mathematics (RICAM) in Linz is looking for PhD student in the field of the optimal control and optimisation. This position is part of the FWF (Austrian Science Fund) project “Numerical verification of optimality and optimality conditions for optimal control problems”.

Requirements: A master’s degree in (applied) mathematics or a closely related field is required. The successful candidate should have an excellent background in applied mathematics, optimization, partial differential equations, and their numerics. Programming skills are desirable.

Salary and Funding: The research is funded by the FWF (Austrian Science Fund) according to its salary guidelines → “FWF Personalkostensätze für DoktorandIn neu”. The position is limited to three years. Funding for conference visits etc. is available. The position can start from September 1, 2009.

Inquiries and applications: Please send the usual documents (CV, degree certificates, thesis – if already finished, title and abstract otherwise, references, and letter of motivation), preferably by email, to

Daniel Wachsmuth
Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Austrian Academy of Sciences
Altenbergerstraße 69
A-4040 Linz, Austria

Project description

Many technical processes are described by partial differential equations. Here, it is important to optimize these processes. This leads to optimization problems in an infinite-dimensional setting.

As model problem, consider the minimization of a functional

g(y)+j(u)

subject to the elliptic equation

-Δy + d(y)=u on Ω, y=0 on Γ

and pointwise control constraints

ua ≤ u ≤ ub

Despite its simple structure, this problem offers many difficulties and challenges. Due to the non-linear elliptic equation this optimisation problem becomes non-convex.

If one has computed solutions yh and uh of discretized versions of this problem, the question arises

Are yh and uh indeed an approximation of a solution of the infinite-dimensional problem?

Due to the inherent non-convexity of the optimization problem, this question by far non-trivial. The project want to give answers to this question with information that is computable from the numerical solution. The methods, which will be applied, are based on techniques from optimal control, finite element methods, and eigenvalue computations.

Official announcement can be obtained from:
http://people.ricam.oeaw.ac.at/d.wachsmuth/projects/

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