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Programme theme
Optimisation problems involving polynomials arise in a wide variety of contexts, including operational research, statistics, probability, finance, computer science, structural engineering, statistical physics, combinatorial chemistry, computational biology and algorithmic graph theory. They are however extremely challenging to solve, both in theory and practice. Existing algorithms and software are capable of solving only very small instances to proven optimality, unless they have some amenable structure, such as sparsity or convexity.
A fascinating feature of polynomial optimisation is that it can be approached from several different directions. In addition to traditional techniques drawn from operational research, computer science and numerical analysis, new techniques have recently emerged based on concepts taken from algebraic geometry, commutative algebra and moment theory. In this regard, polynomial optimisation provides a valuable opportunity for researchers from previously unrelated disciplines to work together.
The plan for this four-week programme is as follows. During the first week (15th-19th July 2013), there will be a "summer school and workshop", which are open not only to official programme participants, but also to other interested academics, PhD students and post-doctoral researchers.
The following three weeks will be open only to invited persons. Each of the three weeks will focus on a specific sub-topic:
1. Algebraic Approaches (22nd-26th July 2013). This will concern the development of new theory and algorithms based on techniques from relevant areas of pure mathematics, such as real algebraic geometry, commutative and noncommutative algebra, moment theory and the theory of sums-of-squares representations.
2. Convex Relaxations and Approximations (29th July-2nd August). This will be devoted to the study of convex relaxations (and hierarchies of relaxations) of certain important specially-structured problem classes, along with associated approximation algorithms (and inapproximability results).
3. Algorithms and Software (5th-9th August). This will be devoted to the development of new algorithms and their implementation as software. This may include, for example, algorithms for computing lower and upper bounds, algorithms for generating strong valid inequalities, and algorithms for solving instances to proven optimality.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme |
|---|---|---|
Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensionsAuthors: Markus Schweighofer, Cordian Riener |
2013 | POP |
Tractable approximations of sets defined with quantifiersAuthors: Jean Bernard Lasserre |
2013 | POP |
On robustness criteria and robust topology optimization with uncertain loadsAuthors: Michal Kocvara |
2013 | POP |
Copositivity for second-order optimality conditions in general smooth optimization problemsAuthors: Immanuel Bomze |
2013 | POP |
Weak orientability of matroids and polynomial equationsAuthors: Jesus De Loera, Jon Lee, S Margulies, J Miller |
2013 | POP |
PENLAB: A MATLAB solver for nonlinear semidefinite optimizationAuthors: J Fiala, Michal Kocvara, M Stingl |
2013 | POP |
Narrowing the difficulty gap for the Celis-Dennis-Tapia problemAuthors: Immanuel Bomze, ML Overton |
2013 | POP |
Copositive relaxation beats Lagrangian dual bounds in quadratically and linearly constrained QPsAuthors: Immanuel Bomze |
2013 | POP |
On global optimization with indefinite quadraticsAuthors: Marcia Fampa, Jon Lee, W Melo |
2013 | POP |
Approximate cone factorizations and lifts of polytopesAuthors: J Gouveia, Pablo A Parrilo, Rekha Thomas |
2013 | POP |
Cutting planes for RLT relaxations of mixed 0-1 polynomial programsAuthors: F Djeumou Fomeni, Konstantinos Kaparis, Adam Letchford |
2013 | POP |
From seven to eleven: completely positive matrices with high CP-rankAuthors: Immanuel Bomze, W Schachinger, R Ullrich |
2013 | POP |
Copositivity-based approximations for mixed-integra fractional quadratic optimizationAuthors: PA Amaral, Immanuel Bomze |
2013 | POP |
New lower bounds and asymptotics for the cp-rankAuthors: Immanuel Bomze, W Schachinger, R Ullrich |
2013 | POP |
Augmentation algorithms for linear and integer linear programmingAuthors: Jesus De Loera, R Hemmecke, Jon Lee |
2013 | POP |
The structure of completely positive matrices according to their CP-rank and CP-plus-rankAuthors: Immanuel Bomze, Peter Dickinson, G Still |
2013 | POP |
Workshops
Polynomial optimisation: workshop and summer school
15 July 2013 to 19 July 2013
Seminars
| Monday 22nd July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Immanuel Bomze Technische Universität Wien |
Room 2 | |
| Tuesday 23rd July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Claus Scheiderer Universität Konstanz |
Room 2 | 
|
| Wednesday 24th July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Jiawang Nie University of California, San Diego |
Room 2 | |
| 17:00 to 20:00 | No Room Required | ||
| Thursday 25th July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Mihai Putinar University of California, Santa Barbara |
Room 2 |
|
| 15:00 to 16:00 |
Dmitrii Pasechnik Nanyang Technological University |
Room 2 | |
| Friday 26th July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Rekha Thomas University of Washington |
Room 2 | |
| Monday 29th July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Renata Sotirov Universiteit van Tilburg |
Room 2 |
|
| Tuesday 30th July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Eden Chlamtac Ben-Gurion University |
Room 2 |
|
| 15:00 to 16:00 |
David Steurer Cornell University |
Room 2 |
|
| Wednesday 31st July 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Peter Dickinson Technische Universität Wien |
Room 2 | |
| Thursday 1st August 2013 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Franz Rendl Alpen-Adria-Universität Klagenfurt |
Room 2 |
|
| 15:00 to 16:00 | Room 2 |
|
|
| Friday 2nd August 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Angelika Wiegele Alpen-Adria-Universität Klagenfurt |
Room 2 | |
| 15:00 to 16:00 |
David Steurer Cornell University |
Room 2 | |
| Monday 5th August 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Jon Lee University of Michigan |
Room 1 |
|
| Tuesday 6th August 2013 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Florian Jarre Heinrich-Heine-Universität Düsseldorf |
Room 1 |
|
| Wednesday 7th August 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Mohab Safey El Din Université Pierre et Marie Curie Paris |
Room 1 |
|
| Thursday 8th August 2013 | |||
|---|---|---|---|
| 12:30 to 13:45 | No Room Required | ||
| 14:00 to 14:15 | Room 1 | ||
| 14:15 to 14:45 |
Miguel Anjos École Polytechnique de Montréal |
Room 1 |
|
| 14:45 to 15:15 | Room 1 |
|
|
| 15:15 to 15:45 |
Designing and tuning RF filters to a prescribed specification |
Room 1 |
|
| 15:45 to 16:15 |
Jakub Marecek IBM Research |
Room 1 |
|
| 16:15 to 16:45 | No Room Required | ||
| 16:45 to 17:15 | Room 1 |
|
|
| 17:15 to 17:45 | Room 1 |
|
|
| 17:45 to 18:30 | Room 1 |
|
|
| 18:30 to 19:30 | No Room Required | ||
| 19:45 to 22:00 | No Room Required | ||
| Friday 9th August 2013 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Houduo Qi University of Southampton |
Room 1 |
|
Organisers
- Jörg Fliege University of Southampton
- Jean Bernard Lasserre Laboratoire d'Analyse et d'Architecture des Systèmes (LAAS)
- Adam Letchford Lancaster University
- Markus Schweighofer Universität Konstanz
Speakers
- Miguel Anjos École Polytechnique de Montréal
- Immanuel Bomze Technische Universität Wien
- Eden Chlamtac Ben-Gurion University
- Peter Dickinson Technische Universität Wien
- Florian Jarre Heinrich-Heine-Universität Düsseldorf
- Jon Lee University of Michigan
- Jakub Marecek University of Nottingham
- Jiawang Nie University of California, San Diego
- Dmitrii Pasechnik Nanyang Technological University
- Mihai Putinar University of California, Santa Barbara
- Houduo Qi University of Southampton
- Franz Rendl Alpen-Adria-Universität Klagenfurt
- Mohab Safey El Din Université Pierre et Marie Curie Paris
- Claus Scheiderer Universität Konstanz
- Renata Sotirov Universiteit van Tilburg
- David Steurer Princeton University
- Rekha Thomas University of Washington
- Angelika Wiegele Alpen-Adria-Universität Klagenfurt
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