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Information für die Wissenschaft Nr. 38 | 13. Juli 2018
Priority Programme “Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization” (SPP 1962)

In March 2015, the Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) established the Priority Programme “Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization” (SPP 1962). The programme is designed to run for six years. Applications are now invited for the second three-year funding period of the programme.

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. The associated non-smoothness typically arises (i) directly in the problem formulation (through non-smooth energies/objectives or system components), (ii) through inequality constraints, nonlinear complementarity or switching systems, or (iii) as a result of competition and hierarchy, typically leading to multiobjective/hierarchical optimization or to quasi-variational inequality problems. In this context, the transition from smoothing or simulation based approaches to genuinely non-smooth techniques or to multi-objective respectively multi-level optimization are crucial. This motivates the research of the programme.

The goals of the Priority Programme are to

  • lay the analytical foundations (through, e.g., the advancement of non-smooth and set-valued analysis),
  • establish a basis for stable numerical approximation through the design of algorithms with mesh independent convergence,
  • address the influence of parameters, which enter the above-mentioned problems and which fall into a specified parameter range (uncertainty set).

The overall research of the Priority Programme aims at combining non-smooth (numerical) analysis of non-linear complementarity, quasi-variational inequality and hierarchical optimization problems, the development, analysis and realization of robust solution algorithms, and applications of large-scale and infinite-dimensional problems where non-smoothness/switching occurs in or are due to

  • systems governing an optimization problem,
  • lower level problems of bi- or multilevel equilibrium problems,
  • coupled systems of equilibrium problems (in particular (generalized) Nash games),
  • systems that require robust solutions,
  • quasi-variational inequalities.

The research of the programme will be validated against prototypical applications. These include: multi-physics problems such as frictional elasto-plastic contact problems in a dynamic regime and coupled with thermal effects; motion optimization and optimal system design in robotics and biomechanics; multi-objective control systems such as (generalized) Nash equilibrium problems in technical or life sciences as well as in economics. Clustered around such proto-typical applications, the research is organized in three communicating research areas:

Area 1. Modelling, problem analysis, algorithm design and convergence analysis.

Area 2. Realization of algorithms, adaptive discretization and model reduction.

Area 3. Incorporation of parameter dependencies and robustness.

The cross section of each of the envisaged research areas exhibits a spectrum from basic research projects to research addressing specific applications. Funded projects typically communicate with at least two areas. Moreover, each project should contribute rigorous mathematical analysis to the overall Priority Programme. Further information concerning the research orientation of the programme can be found on the programme’s website.

Besides individual projects, joint proposals (involving typically two groups) are welcome. From the work programme within the proposal it should become clear which parts are assigned to which scientific coworker, especially which tasks should be fulfilled by PhD students or postdocs. In case of joint proposals the assignment of requested funds to the individual principal investigators (PI) should also become clear. The proposals should also indicate how they fit into the programme as a whole.

As a follow-up measure of the DFG-AIMS-Workshop on “Shape optimization, homogenization and control” (13–16 March 2017 at AIMS Sénégal in Mbour) an additional budget has been allocated in the context of this Priority Programme to fund joint research projects between scientists in Germany and Africa in the areas of shape optimization, homogenization and control. Regarding the content, these proposals do not necessarily have to fulfill all the requirements set above for fundable core projects within Priority Programme 1962. It is not mandatory that the partners and PI from Germany and Africa attended the DFG-AIMS-Workshop in 2017. In the case of African partners from developing countries, proposals in the frame of DFG’s programme “Cooperation with Developing Countries” may be submitted (see link below). Salary supplements for PI from Africa cannot be applied for. Funding can only be allocated to project partners in Germany and Africa. Participation of scientists from other countries is possible, but must be funded from other sources. Applications must be written in English and submitted by the Germany project partner(s). African project partners cannot propose independently without German scientists. German and African partners form a consortium and will in the case of approval each receive funding according to the project requirements, but German partner(s) are responsible for channelling funds to Africa for legal reasons.

Proposals for the second three-year funding period of the Priority Programme 1962 or African-German cooperation projects in the areas of shape optimization, homogenization and control have to be submitted starting 17 October and no later than 31 October 2018. They have to be submitted via the DFG’s portal elan selecting “SPP 1962”. If you are using the submission system for the first time, please note that you need to register yourself and your institutional address before being able to submit a proposal. Also, if you are planning to move to a different institution (e.g. with a temporary position as principal investigator) you need to update your institutional address beforehand. The registration of a new account needs to be confirmed manually by DFG and is requested no later than 24 October 2018. The proposals have to be submitted in English, and need to be prepared using the respective forms and guidelines in English language.

General information on proposals in the framework of a Priority Programme (in particular concerning eligibility and admissible funding requests) can be found in guideline 50.05 (part B). See also guideline 54.01 for instructions how to prepare a proposal. The specific proposal has to be structured according to form 53.01. However, it is admissible to prepare the proposal as a pdf-file, e.g., using LaTeX, instead of using the rtf-file which is available online.

A review meeting with international reviewers and applicants will be held on 7–8 March 2019 in Berlin. The envisaged start of funding is mid-2019.

Further Information

Further information on the Priority Programme is available at:

For the DFG’s programme “Cooperation with Developing Countries” please refer to:

The elan system can be accessed at:

DFG forms 50.05, 53.01 and 54.01 can be accessed at:

For further scientific information, please contact the Priority Programme’s coordinator:

  • Prof. Dr. Michael Hintermüller,
    Institute for Mathematics,
    Humboldt-University of Berlin,
    10099 Berlin, Germany,
    phone +49 30 2093-2668,

For administrative and formal inquiries please contact at the DFG Head Office:


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