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Algorithms and software for structured Semidefinite Optimization problems

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  • Full or part time
    Prof M Kocvara
  • Application Deadline
    Applications accepted all year round

Project Description

This project is part of the HORIZON 2020 Marie Skłodowska-Curie Innovative Training Network "POEMA, Polynomial Optimization, Efficiency through Moments and Algebra", which is offering 15 PhD positions, starting from September 2019 (more about POEMA below and here

Objectives of this project: The classical moment-SOS SDP hierarchy for Polynomial Optimization, although general and very powerful, is limited to problems of small to medium size only. This is due to the rapidly growing size of SDP problems that become unsolvable by the state of the art general purpose SDP software, such as MOSEK or PENSDP. While the SDP problems arising in the moment-SOS hierarchy have a specific structure, this structure cannot be utilized by the general purpose software. The way to use this specific structure was first shown by Kojima and his co-authors in their works on so-called sparse-POP problems. The goal of this project is to substantially extent the sparse-POP approach to various SDP problems arising in other work packages and beyond. We will use and extend the techniques of matrix completion and chordal sparsity in order to decompose the SDP problems either with large matrix variables or with large matrix constraints into problems with many small matrix variables or matrix constraints. The decomposed problems can then be solved much more efficiently by existing general purpose SDP software, as documented in current literature. We will a) extend the existing theory of matrix completion and matrix decomposition to new classes of matrices; b) develop corresponding algorithms for matrix decomposition and c) develop corresponding software. The software development will follow two lines: a) stand-alone software for matrix decomposition, whose outcome is an SDP problem solvable by general purpose SDP software such as MOSEK; b) software for matrix decomposition built in a modified version of the existing code PENSDP developed by the applicants. The resulting software will be tested using benchmark problems and, when applicable, industrial applications collected from other work packages.


Its goal is to train scientists at the interplay of algebra, geometry and computer science for polynomial optimization problems and to foster scientific and technological advances, stimulating interdisciplinary and intersectoriality knowledge exchange between algebraists, geometers, computer scientists and industrial actors facing real-life optimization problems.

The network partners are

Inria, Sophia Antipolis, France, (Bernard Mourrain)
CNRS, LAAS, Toulouse France (Didier Henrion)
Sorbonne Université, Paris, France (Mohab Safey el Din)
NWO-I/CWI, Amsterdam, the Netherlands (Monique Laurent)
Univ. Tilburg, the Netherlands (Etienne de Klerk)
Univ. Konstanz, Germany (Markus Schweighofer)
Univ. degli Studi di Firenze, Italy (Giorgio Ottaviani)
Univ. of Birmingham, UK (Michal Kocvara)
Friedrich-Alexander-Universitaet Erlangen, Germany (Michael Stingl)
Univ. of Tromsoe, Norway (Cordian Riener)
Artelys SA, Paris, France (Arnaud Renaud)
The associate partners are

IBM Research, Ireland (Martin Mevissen)
NAG, UK (Mike Dewar)
RTE, France (Jean Maeght)

Funding Notes

Submission guidelines can be found here:

Trans-national mobility: The applicant — at the date of recruitment — should not have resided in the country where the research training takes place for more than 12 months in the 3 years immediately prior to recruitment, and not have carried out their main activity (work, studies, etc.) in that country. For refugees under the Geneva Convention (1951 Refugee Convention and the 1967 Protocol), the refugee procedure (i.e. before refugee status is conferred) will not be counted as ‘period of residence/activity in the country of the beneficiary’.

How good is research at University of Birmingham in Mathematical Sciences?

FTE Category A staff submitted: 40.00

Research output data provided by the Research Excellence Framework (REF)

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