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TAMING SIGNED

Taming non convexity?

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EC-Contrib. €

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Partnership

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Project "TAMING" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Project website http://www.taming.laas.fr
 Total cost 1˙450˙625 €
 EC max contribution 1˙450˙625 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2019-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙450˙625.00

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 Project objective

In many important areas and applications of science one has to solve non convex optimization problems and ideally and ultimately one would like to find the global optimum. However in most cases one is faced with NP-hard problems and therefore in practice one has been often satisfied with only a local optimum obtained with some ad-hoc (local) optimization algorithm.

TAMING intends to provide a systematic methodology for solving hard non convex polynomial optimization problems in all areas of science. Indeed the last decade has witnessed the emergence of Polynomial Optimization as a new field in which powerful positivity certificates from real algebraic geometry have permitted to develop an original and systematic approach to solve (at global optimality) optimization problems with polynomial (and even semi-algebraic) data. The backbone of this powerful methodology is the « moment-SOS » approach also known as « Lasserre hierarchy » which has attracted a lot of attention in many areas (e.g., optimization, applied mathematics, quantum computing, engineering, theoretical computer science) with important potential applications. It is now a basic tool for analyzing hardness of approximation in combinatorial optimization and the best candidate algorithm to prove/disprove the famous Unique Games Conjecture. Recently it has also become a promising new method for solving the important Optimal Power Flow Problem in the strategic domain of Energy Networks (as the only method that could solve to optimality certain types of such problems).

However in its present form this promising methodology inherits a high computational cost and a (too) severe problem size limitation which precludes from its application many important real life problems of significant size. Proving that indeed this methodology can fulfill its promises and solve important practical problems in various areas poses major theoretical & practical challenges.

 Publications

year authors and title journal last update
List of publications.
2019 Jean B. Lasserre, Youssouf Emin
Semidefinite Relaxations for Lebesgue and Gaussian Measures of Unions of Basic Semialgebraic Sets
published pages: , ISSN: 0364-765X, DOI: 10.1287/moor.2018.0980
Mathematics of Operations Research 2019-09-26
2019 Jean B. Lasserre, Tillmann Weisser
Distributionally robust polynomial chance-constraints under mixture ambiguity sets
published pages: , ISSN: 0025-5610, DOI: 10.1007/s10107-019-01434-8
Mathematical Programming 2019-09-20
2019 Simon Foucart, Jean Bernard Lasserre
Computation of Chebyshev Polynomials for Union of Intervals
published pages: , ISSN: 1617-9447, DOI: 10.1007/s40315-019-00285-w
Computational Methods and Function Theory 2019-08-29
2018 Cédric Josz, Daniel K. Molzahn
Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables
published pages: 1017-1048, ISSN: 1052-6234, DOI: 10.1137/15M1034386
SIAM Journal on Optimization 28/2 2019-07-02
2017 Didier Henrion, Simone Naldi, Mohab Safey El Din
SPECTRA – a Maple library for solving linear matrix inequalities in exact arithmetic
published pages: 1-17, ISSN: 1055-6788, DOI: 10.1080/10556788.2017.1341505
Optimization Methods and Software 2019-07-02
2016 Jean B. Lasserre
A MAX-CUT formulation of 0/1 programs
published pages: 158-164, ISSN: 0167-6377, DOI: 10.1016/j.orl.2015.12.014
Operations Research Letters 44/2 2019-07-02
2017 Milan Korda, Didier Henrion
Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets
published pages: , ISSN: 1862-4472, DOI: 10.1007/s11590-017-1186-x
Optimization Letters 2019-07-02
2017 Milan Korda, Didier Henrion, Colin N. Jones
Convergence rates of moment-sum-of-squares hierarchies for optimal control problems
published pages: 1-5, ISSN: 0167-6911, DOI: 10.1016/j.sysconle.2016.11.010
Systems & Control Letters 100 2019-07-02
2017 Jean B. Lasserre, Kim-Chuan Toh, Shouguang Yang
A bounded degree SOS hierarchy for polynomial optimization
published pages: 87-117, ISSN: 2192-4414, DOI: 10.1007/s13675-015-0050-y
EURO Journal on Computational Optimization 5/1-2 2019-07-02
2015 Jean B. Lasserre
Moments and Legendre-Fourier Series for Measures Supported on Curves
published pages: , ISSN: 1815-0659, DOI: 10.3842/SIGMA.2015.077
Symmetry, Integrability and Geometry: Methods and Applications 11 2019-07-02
2017 Jean B. Lasserre
Representation of Chance-Constraints With Strong Asymptotic Guarantees
published pages: 50-55, ISSN: 2475-1456, DOI: 10.1109/LCSYS.2017.2704295
IEEE Control Systems Letters 1/1 2019-07-02
2017 Jean B. Lasserre
Computing Gaussian & exponential measures of semi-algebraic sets
published pages: 137-163, ISSN: 0196-8858, DOI: 10.1016/j.aam.2017.06.006
Advances in Applied Mathematics 91 2019-07-02
2016 V. Jeyakumar, J. B. Lasserre, G. Li, T. S. Phạm
Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems
published pages: 753-780, ISSN: 1052-6234, DOI: 10.1137/15M1017922
SIAM Journal on Optimization 26/1 2019-07-02
2016 Edouard Pauwels, Didier Henrion, Jean-Bernard Lasserre
Linear Conic Optimization for Inverse Optimal Control
published pages: 1798-1825, ISSN: 0363-0129, DOI: 10.1137/14099454X
SIAM Journal on Control and Optimization 54/3 2019-07-02
2018 Simon Foucart, Jean B. Lasserre
Determining projection constants of univariate polynomial spaces
published pages: 74--91, ISSN: 0021-9045, DOI: 10.1016/j.jat.2018.06.002
Journal of Approximation Theory 2019-07-02
2017 Etienne de Klerk, Jean B. Lasserre, Monique Laurent, Zhao Sun
Bound-Constrained Polynomial Optimization Using Only Elementary Calculations
published pages: 834-853, ISSN: 0364-765X, DOI: 10.1287/moor.2016.0829
Mathematics of Operations Research 42/3 2019-07-02
2017 Tillmann Weisser, Jean B. Lasserre, Kim-Chuan Toh
Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity
published pages: 1-32, ISSN: 1867-2949, DOI: 10.1007/s12532-017-0121-6
Mathematical Programming Computation 2019-07-02
2019 Jean B. Lasserre
Volume of Sublevel Sets of Homogeneous Polynomials
published pages: 372-389, ISSN: 2470-6566, DOI: 10.1137/18m1222478
SIAM Journal on Applied Algebra and Geometry 3/2 2019-06-07
2018 Jean B. Lasserre, Mihai Putinar
Positive functionals and Hessenberg matrices
published pages: 1, ISSN: 0002-9939, DOI: 10.1090/proc/14266
Proceedings of the American Mathematical Society 2019-05-23
2019 Swann Marx, Tillmann Weisser, Didier Henrion, Jean Bernard Lasserre
A moment approach for entropy solutions to nonlinear hyperbolic PDEs
published pages: 0-0, ISSN: 2156-8472, DOI: 10.3934/mcrf.2019032
Mathematical Control & Related Fields 0/0 2019-05-27
2018 Jean-Bernard Lasserre, Victor Magron
Optimal Data Fitting: A Moment Approach
published pages: 3127-3144, ISSN: 1052-6234, DOI: 10.1137/18m1170108
SIAM Journal on Optimization 28/4 2019-05-22
2019 Jean B. Lasserre, Edouard Pauwels
The empirical Christoffel function with applications in data analysis
published pages: 1--30, ISSN: 1019-7168, DOI: 10.1007/s10444-019-09673-1
Advances in Computational Mathematics 2019-04-18
2019 Cédric Josz, Jean Bernard Lasserre, Bernard Mourrain
Sparse polynomial interpolation: sparse recovery, super-resolution, or Prony?
published pages: , ISSN: 1019-7168, DOI: 10.1007/s10444-019-09672-2
Advances in Computational Mathematics 2019-04-18
2017 Yohann De Castro, F. Gamboa, Didier Henrion, J.-B. Lasserre
Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions
published pages: 621-630, ISSN: 0018-9448, DOI: 10.1109/tit.2016.2619368
IEEE Transactions on Information Theory 63/1 2019-02-28
2019 Yohann De Castro, Fabrice Gamboa, Didier Henrion, Roxana Hess, Jean-Bernard Lasserre
Approximate optimal designs for multivariate polynomial regression
published pages: 127-155, ISSN: 0090-5364, DOI: 10.1214/18-aos1683
The Annals of Statistics 47/1 2019-02-25
2019 Jean-Bernard Lasserre, Victor Magron
In SDP Relaxations, Inaccurate Solvers Do Robust Optimization
published pages: 2128-2145, ISSN: 1052-6234, DOI: 10.1137/18m1225677
SIAM Journal on Optimization 29/3 2019-09-05

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