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Final Activity Report Summary - ADONET (Algorithmic discrete optimisation)

The aims of the Marie Curie network "Algorithmic Discrete Optimisation" were twofold: On the one hand, it was the task of the consortium to bring forward the research in Integer Programming, Convex Programming and Combinatorial Optimisation, all of which constitute important and actively growing fields of mathematics reaching out to natural and social sciences, engineering and industry. On the other hand, the participants from ten countries took all efforts to promote research training in the relevant fields of the project, to facilitate transfer-of-knowledge activities both among the participating institutions and together with industrial partners, and to open up career opportunities to young researchers. During the project, 77 young researchers have been hired reaching a proportion of 21 % of female researchers. About 75% of the researchers came from EU- or associated countries.

Speaking of research, highlights in Integer Programming include the connection made between lattice point free polyhedra and mixed-integer cutting plane theory. Another important result concerns a breakthrough in the linear description of the stable-set polytope for claw-free graphs. Significant progress has also been made in the field of nonlinear programming for both integer and mixed integer formulations including the formulation of fully polynomial time approximation schemes (FPTAS). Moreover, interesting new results have been achieved for solving polynomial optimisation problems based on sums of squares of polynomials and moment theory combined with semidefinite programming.

Outstanding results in Convex Programming include the use of symmetry reduction to find better bounds on the size of error correcting code and a polynomial time approximation scheme (PTAS) for the inimisation of a polynomial on the simplex. Among the highlights in Combinatorial Optimisation are recent results on orientations of graphs achieving high connectivity and advances concerning submodular functions and the matroid parity problem.

Research training was established on several levels starting with regular seminars at the participants' sites. In addition to local events, ESRs and ERs took part in scientific meetings and conferences outside their research group, and they participated in training events organised within ADONET. The latter include seven doctoral school and an advanced workshop on modelling and solving with Xpress-MP, organised by the Dash group, the industrial participant in the network. Moreover the recruited researchers learnt to improve their soft skills, and many of them started to learn a foreign language or to improve their knowledge of it.

As a whole, the network had an important influence on the international scientific community. Firstly, on a variety of international conferences and other occasions, ADONET activities and vacancies were announced, thus attracting researchers and visitors coming from non-ADONET sites to ADONET events. Secondly, the interaction between ADONET partners was triggered a lot, resulting both in joint publications and short-time visits of senior researchers at other ADONET sites. Thirdly, the network regularly hosted senior researchers from other places, both within Europe and from outside. These guests were usually also involved in the training aspects of ADONET as they, for instance, gave lectures at the doctoral schools and organised local minicourses so that the young researchers could profit from their expertise.

The research activities of the network have been internationally recognised. In particular, in 2005 Alexander Schrijver received the notable Spinoza Prize for his 'excellent, innovating and inspiring research' in the field of combinatorics and algorithms, and Robert Weismantel was conferred an IBM Academic Award in 2007 for his research in nonlinear mixed-integer optimisation. As another aspect, several of the ESRs and ERs have obtained leading positions in academia and industry.

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