Address : CWI Science Park 123 1098 XG Amsterdam The Netherlands Postal address: CWI, Postbus 94079, 1090 GB Amsterdam Phone : +31 20 5924105 (office) +31 20 5929333 (reception) +31 20 5924189 (secretary) Email : monique at cwi dot nl Office : M233 how to reach CWI Google map

Research group

Since September 1, 2009, I am also affiliated as (part-time) full professor at the Department of Econometrics and Operations Research
of * Tilburg University*.
Link to my
CentER page.

See here for the research group seminar

and here for the

**EU Project TENORS:**

The EU Marie Sklodowska-Curie Joint Doctoral Network TENORS (Tensor modEliNg, geOmetRy and optimiSation) runs from January 2024 to December 2027. See the webpage of TENORS and the list of PhD positions supported by TENORS, including DC12 at CWI (supervised by Monique Laurent, jointly with Victor Magron at LAAS-CNRS, Toulouse), and DC6 at MPI-Leipzig (supervised by Bernd Sturmfels, Simon Telen, jointly with Monique Laurent at CWI, Amsterdam).

See the call for papers in a special issue of the journal * Numerical Algebra, Control and Optimization (NACO) * (submission deadline: **30 April 2024**). The issue is devoted to recent developments in convex or polynomial optimization and their applications.

Mastermath course: ** Semidefinite Optimization**, spring 2024.

LNMB course: Networks and Semidefinite Programming, fall 2024.

Oberwolfach Workshop on Combinatorial Optimization, 10-15 November 2024.

IWOTA 2024 - International Workshop on Operator Theory and its Applications, Canterbury, 12-16 August 2024.

Workshop for Bernard Mourrain's 60th Birthday, MPI Leipzig, 3 August 2024.

Oberwolfach Workshop Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms, and Applications, 28 July-2 August 2024.

Gauss Lecture, Klagenfurt, 25 June 2024.

MoPAT24 - Moments and Polynomials: Applications and Theory, Konstanz, 11-14 March 2024.

OPTIMAL Conference, UvA, 19 December 2023.

POP23 - Future Trends in Polynomial OPtimization, LAAS-CNRS Toulouse, 13-17 November 2023.

See also the call for papers in a special issue of the journal * Numerical Algebra, Control and Optimization (NACO) * (submission deadline: **30 April 2024**).

Workshop
Algebraic Techniques for Optimization, CWI, 2 November 2023.

Geometry of Polynomial System Solving, Optimization and Topology, IHP Paris, 16-20 October 2023.

Symposium `Special functions and their applications', at the occasion of the 80-th birthday of Tom Koornwinder. University of Amsterdam, 15 September 2023.

ICIAM 2023, Tokyo, 20-15 August 2023.

SIAM Conference on Applied Algebraic Geometry (SIAM AG 23), TU Eindhoven,
10-14 July 2023.

NMC 2023, 11-12 April 2023.

- Preprints
- Book
- Surveys
- Recent publications
- Editorial work
- Some slides of talks
- Organization of workshops
- Recent events
- Recent teaching
- Research networks

* Notes on the paper:
``Convergence of SDP hierarchies for polynomial
optimization on the hypersphere",
by A.C. Doherty and S. Wehner.*
Unpublished paper.

*
Semidefinite programming formulations for the completely bounded norm of a tensor.*
With S. Gribling.
Preprint at arXiv,
January 2019.

Geometry of Cuts and Metrics (with M.M. Deza).
Springer-Verlag, Berlin, 1997.

Softcover publication in 2010. See the
book's flyer.

Book review in Optima 56 .

[Corrections can be found here.]

* Copositive matrices, sums of squares and the stability number of a graph.* With Luis Felipe Vargas. Preprint at arXiv, 2023.
In:
Polynomial Optimization, Moments, and Applications.
M. Kocvara, B. Mourrain, C. Riener (eds).
Springer Optimization and Its Applications (SOIA, volume 206), pages 99--132, 2023.

*Optimization over polynomials: Selected topics. *
In Chapter 16 (Control Theory and Optimization) of Proceedings of the International Congress of Mathematicians 2014 (ICM 2014). Jang, S. Y., Kim, Y. R., Lee, D-W. & Yie, I. (eds.). Seoul: Kyung Moon SA Co. Ltd., p. 843-869, 2014.
File here.

*Copositive vs. moment hierarchies for stable sets.*
Discussion column, Optima 89, Mathematical Optimization Society Newsletter, 2012.
Link here.

* The Approach of Moments for Polynomial Equations. *
With P. Rostalski.
Chapter 2 in * Handbook on Semidefinite, Cone and Polynomial Optimization,* M. Anjos and J.B. Lasserre (eds.),
International Series in Operations Research & Management Science, 2012, Volume 166, Part 1, 25-60.
Springer
link and
file (version, September 2010).

*Semidefinite programming approximations for stable sets, colouring, and cuts in graphs.*
ps-file, January 2009, NVTI Newsletter.

* Sums of squares, moment matrices and optimization over polynomials.*
In *Emerging Applications of Algebraic Geometry*, Vol. 149 of
*IMA Volumes
in Mathematics and its Applications,*
M. Putinar and S. Sullivant (eds.), Springer, pages 157-270, 2009.
File.

[Corrections can be found
here.]

Updated version
here,
dated February 6, 2010.

* Arbres et coupes de poids minimum*. In * Graphes et Applications 1*, J.-C. Fournier (ed.), Hermes, Lavoisier, Paris, pages 225-261, 2007.

* Semidefinite Programming and Integer Programming. *
With F. Rendl.
In
* Handbook on Discrete Optimization, *
K. Aardal, G. Nemhauser, R. Weismantel (eds.),
pages 393-514, Elsevier B.V., December 2005.
File.

* Matrix completion problems. *
In The Encyclopedia of Optimization, vol. III (Interior - M),
pages 221-229.
C.A. Floudas and P.M. Pardalos, editors, Kluwer, 2001.
File.

* Notes on Binary Spaces.*
Unpublished manuscript, 102 pages, 1998.
File.

* A tour d'horizon on positive semidefinite and Euclidean
distance matrix completion problems.*
In P. Pardalos and H. Wolkowicz, editors,
Topics in Semidefinite and Interior-Point Methods,
volume 18 of The Fields Institute for Research
in Mathematical Science, Communications
Series. Providence, Rhode Island, pages 51--76, 1998.

* Max-Cut Problem.*
Chapter in * Annotated Bibliographies in Combinatorial Optimization,
*
edited by M. Dell'Amico, F. Maffioli and S. Martello.
John Wiley, pages 241-259, 1997.

* Semidefinite approximations for bicliques and biindependent pairs.*
With Sven Polak and Luis Felipe Vargas.
* Mathematics of Operations Research*, published online: 13 March 2024.
Paper and preprint at
arXiv.

* Exploiting ideal-sparsity in the generalized moment problem with
application to matrix factorization ranks.*
With Milan Korda, Victor Magron, and Anderies Steenkamp.
Mathematical Programming, 205:703--744, 2024. Paper and preprint at arXiv.

* Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph. * With Luis Felipe Vargas.
Mathematics of Operations Research, 48(2):1017--1043, 2023.
Paper and preprint at arXiv.

* On the exactness of sum-of-squares approximations for the cone of 5x5 copositive matrices. *
With Luis Felipe Vargas.
Linear Algebra and its Applications, 651:26-50, 2022. Paper and Preprint at arXiv.

An effective version of Schm\"udgen's Positivstellensatz for the hypercube. With Lucas Slot.
* Optimization Letters*, 17:515-530, 2023.
Preprint at arXiv.

* Finite convergence of sum-of-squares hierarchies for the stability number of a graph.*
With Luis Felipe Vargas.
*SIAM Journal on Optimization*, 32(2):491--518, 2022.
Preprint at arXiv.

*
Bounding the separable rank via polynomial optimization.
*
With Sander Gribling and Andries Steenkamp.
*Linear Algebra and its Applications*, 648:1--55, 2022.
Preprint at arXiv.

* Optimizing hypergraph-based polynomials
modeling job-occupancy in queueing with
redundancy scheduling.* With Daniel Brosch and Andries Steenkamp.
* SIAM Journal on Optimization,* 31(3):2227-2254, 2021.
Paper and
preprint at arXiv.

* Sum-of-squares hierarchies for binary polynomial optimization.*
With Lucas Slot. Full final paper, *Mathematical Programming*, 197:621--660, 2023.
arXiv paper.

* Sum-of-squares hierarchies for binary polynomial optimization.*
With Lucas Slot.
In: Singh M., Williamson D.P. (eds) Integer Programming and Combinatorial Optimization.
Paper at IPCO 2021.
Lecture Notes in Computer Science, vol 12707, pp. 43-57. Springer, Cham. https://doi.org/10.1007/978-3-030-73879-2_4

* Near-optimal analysis of univariate moment bounds for polynomial
optimization. * With Lucas Slot.
* Mathematical Programming,* 188, pp. 443-460, 2021.
Final paper.
Preprint at arXiv.

* Improved convergence analysis of Lasserre's measure-based upper bounds for polynomial minimization on compact sets*.
With Lucas Slot.
* Mathematical Programming*, 193:831-871, 2022.
Final paper.
Preprint at arXiv.

* Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere*. With E. de Klerk.
* Mathematical Programming*, 193:665-685, 2022.
Final paper.
Preprint at arXiv.

* Worst-case examples for Lasserre's measure--based hierarchy for polynomial optimization on the hypercube.*
With E. de Klerk.
* Mathematics of Operations Research,* 45(1):86-98, 2020.
Paper and
arXiv.

*A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis.*
With E. de Klerk.
In: Araujo C., Benkart G., Praeger C., Tanbay B. (eds), World Women in Mathematics 2018. Association for Women in Mathematics Series, vol 20. Springer, Cham (2019).
Publisher,
final paper
and
arXiv.

Please see here for an erratum about the statements and proofs of Theorems 9 and 11.

*
Lower bounds on matrix factorization ranks via noncommutative polynomial
optimization.*
With S. Gribling and D. de Laat.
* Foundations of Computational Mathematics.*
19:1013-1070, 2019.
Paper here.

*
Comparison of Lasserre's measure--based bounds for polynomial optimization to bounds obtained by simulated annealing.*
With E. de Klerk.
* Mathematics of Operations Research.* 43:1317-1325, 2018.
Preprint at arXiv.

*
Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization.*
With S. Gribling and David de Laat.
* Mathematical Programming*. 170(1):5--42, 2018.
Paper.

*
On the Linear Extension Complexity of Stable Set Polytopes for Perfect Graphs.*
With Hao Hu.
*European Journal of Combinatorics.* (80): 247-260, 2019.
Final paper available
here;
preprint at
arXiv.

*
Perfect Elimination Orderings for Symmetric Matrices.*
With S. Tanigawa.
* Optimization Letters*, pages 1-15, 2017.
First online.

* Similarity-First Search: a new algorithm with application to Robinsonian matrix recognition.*
With M. Seminaroti.
* SIAM Journal on Discrete Mathematics.* 31(3):1765-1800, 2017.
Paper
here.
and at arXiv.

The code for the ** Similarity-First Search (SFS) Seriation algorithm** is available at
the R platform.

*
A Lex-BFS-based recognition algorithm for Robinsonian matrices.*
With M. Seminaroti. *Discrete Applied Mathematics,*
222:151-165, 2017.
Preprint at
arXiv.

*
A Structural Characterization for Certifying Robinsonian Matrices.*
With M. Seminaroti and S. Tanigawa.
* Electronic Journal of Combinatorics,* 24(2),
Paper #P2.21, 2017.

* Improved convergence rates for Lasserre-type hierarchies of upper bounds for box-constrained polynomial optimization.*
With E. de Klerk and R. Hess.
* SIAM Journal on Optimization,* 27(1), 347--367, 2017.
Preprint at arXiv.

* Bound-constrained polynomial optimization using only elementary calculations*. With E. de Klerk, J. Lasserre and Z. Sun.
* Mathematics of Operations Research,*
42(3):834--853.
Published Online: March 15, 2017.
Preprint at arXiv.

* On the closure of the completely positive semidefinite cone and linear
approximations to quantum colorings.*
With S. Burgdorf and T. Piovesan.
* The Electronic Journal of Linear Algebra,* 32:15--40, 2017.
Preprint at
arXiv
and final paper at ELA.

* Matrices with high completely positive semidefinite rank. *
With D. de Laat and S. Gribling.
*Linear Algebra and its Applications*, 513:122-148, 2017.
Preprint at
arXiv.

*Convergence analysis for Lasserre's measure-based hierarchy of upper bounds for polynomial optimization.*
With E. de Klerk and Z. Sun. *Mathematical Programming Series A*
162(1): 363-392, 2017.
Preprint at arXiv.

* On the convergence rate of grid search for polynomial optimization over the simplex*. With E. de Klerk, J.C. Vera and Z. Sun.
* Optimization Letters,* 11(3):597-608, 2017.
Preprint at
arXiv.

* Conic approach to quantum graph parameters using linear
optimization over the completely positive semidefinite
cone.*
With T. Piovesan.
* SIAM Journal on Optimization*, 25(4):2461--2493, 2015.
arXiv.

* An error analysis for polynomial optimization over the simplex based on
the multivariate hypergeometric distribution.*
With E. de Klerk and Z. Sun.
* SIAM Journal on Optimization*, 25(3):1498--1514, 2015.
Paper and
arXiv.

* A Lex-BFS-based recognition algorithm for Robinsonian
matrices.*
Extended abstract.
In Algorithms and Complexity: Proceedings of the 9th International Conference
CIAC 2015, volume 9079 of Lecture Notes in Computer Science, pages 325-338. Springer-
Verlag, 2015.
File.

*Entanglement-assisted zero-error source-channel coding.*
With J. Briet, H. Buhrman, T.Piovesan and G. Scarpa.
* IEEE Transactions on Information Theory*, 61(2):1--15, 2015.
Preprint at arXiv.
(Extended abstract published at Eurocomb 2013.)

* The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure.*
With M. Seminaroti.
* Operations Research Letters,* 43(1):103--109, 2015.
Preprint at arXiv:1407.2801v2.

* An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex.*
With E. de Klerk and Z. Sun.
*Mathematical Programming Ser. B.*
Published online: 15 October 2014.
Preprint at
arXiv.

*Forbidden minor characterizations for low-rank optimal
solutions to semidefinite programs over the elliptope.*
With M. E.-Nagy and A. Varvitsiotis,
file,
*Journal of Combinatorial Theory B,*
108:40-80, 2014.

(Revised version of the earlier preprint:
* On bounded rank positive semidefinite matrix completions of extreme partial correlation matrices.*
arXiv:1205.2040, 2012.)

* Positive semidefinite matrix completion, universal rigidity and the Strong Arnold Property.*
With A. Varvitsiotis.
* Linear Algebra and its Applications,*
452:292--317, 2014.
arXiv:1301.6616,

*Handelman 's hierarchy for the maximum stable set problem.*
With Zhao Sun.
Journal of Global Optimization, 60(3):393-423, 2014.
Preprint at arXiv:1305.7319.

* Complexity of the positive semidefinite matrix completion problem with a rank constraint.*
With M. E.-Nagy and A. Varvitsiotis.
In * Discrete Geometry and Optimization*, Volume 69 of Fields Institute Communications, K. Bezdek, A. Deza and Y. Ye (eds),
Springer, pages 105--120, 2013.
Preprint at arXiv:1203.6602.

* A new graph parameter related to bounded rank positive semidefinite matric completions.*
With A. Varvitsiotis.
Mathematical Programming, Ser. A., Volume 145, Issue 1-2, pp 291-325, June 2014.
Preprint at arXiv:1204.0734.

* Moment matrices, border bases and radical computation.*
With J.B. Lasserre, B. Mourrain, Ph. Rostalski and Ph. Trebuchet.
*Journal of Symbolic Computation,* 51, 63-85, 2013.
Preprint at arXiv:1112.3197.

*The Gram dimension of a graph*. With A. Varvitsiotis.
In Proceedings of the 2nd International Symposium on Combinatorial Optimization. A.R. Mahjoub et a. (Eds.): ISCO 2012, LCS 7422, pp. 356--367, 2012.
Preprint at arXiv:1112.5960.

* A new semidefinite programming relaxation for cycles in binary matroids and cuts in graphs.*
With J. Gouveia, P. Parrilo and R. Thomas.
* Mathematical Programming,* 112(1-2), 203-225, 2012.
arXiv:0907.4518.

* Computing the Grothendieck constant of some graph classes.*
With A. Varvitsiotis.
* Operations Research Letters*, Volume 39, Issue 6, November 2011, Pages 452-456.
Preprint.

* On the Lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems.*
With E. de Klerk.
* SIAM Journal on Optimization*, 21, 824-832, 2011.
File.

* On Leonid Gurvits's proof for permanents.*
With A. Schrijver.
*The American Mathematical Monthly,* 117(10): 903-911, 2010.
File.

* Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube.*
With E. de Klerk.
* SIAM Journal on Optimization,* 20(6):3104-3120, 2010.
File

*A generalized flat extension theorem for moment matrices.*
With B. Mourrain.
* Archiv der Mathematik,* 93(1):87--98, July 2009.
File.

*A prolongation-projection algorithm for computing the finite real variety of an ideal.*
With J. Lasserre and P. Rostalski,
* Theoretical Computer Science* 410(27-29):2685-2700, 2009.
File.

* Block-diagonal semidefinite programming hierarchies for 0/1 programming.* With N. Gvozdenovic and F. Vallentin.
* Operations Research Letters* 37:27-31, 2009.
File.

* A unified approach to computing real and complex zeros
of zero-dimensional ideals.* with J.B. Lasserre and P. Rostalski.
In *Emerging Applications of Algebraic Geometry*, Vol. 149 of
*IMA Volumes
in Mathematics and its Applications,*
M. Putinar and S. Sullivant (eds.), Springer, pages 125-155, 2009.
File.

* Semidefinite Programming in Combinatorial and Polynomial Optimization.*
* Nieuw Archief voor Wiskunde*, NAW 5/9 nr. 4, December 2008.
File.

* The operator $\Psi$ for the Chromatic Number of a Graph.*
With N. Gvozdenovic.
* SIAM Journal on Optimization* 19(2):572-591, 2008.
File.

*Computing semidefinite programming lower bounds for the (fractional)
chromatic number via block-diagonalization.*
With N. Gvozdenovic.
* SIAM Journal on Optimization * 19(2):592-615, 2008.
File.

* Computing the real variety of an ideal - A real algebraic and symbolicnumeric algorithm. *
With J.-B. Lasserre and P. Rostalski.
In * SAC'08: Proceedings of the 2008 ACM Symposium on Applied Computing*,
pages 1845--1846, Fortaleza, Brazil, 2008.

* Semidefinite characterization and computation of
zero-dimensional real radical ideals*, with J.-B. Lasserre and P. Rostalski.
* Foundations of Computational Mathematics*,
8(5):607--647, 2008.
Link.

Semidefinite representations for finite varieties.
* Mathematical Programming*, 109:1--26, 2007.
File.

Strengthened semidefinite programming bounds for codes.
* Mathematical Programming,* 109(2-3):239-261, 2007.

New Limits on Fault-Tolerant Quantum Computation.
With H. Buhrman, R. Cleve, N. Linden, A. Schrijver and F. Unger.
In: 47th Annual IEEE Symposium on Foundations of Computer Science
(FOCS 2006),
pp. 411-419.

A PTAS for the minimization of polynomials
of fixed degree over the simplex.
With E. De Klerk and P. Parrilo.
* Theoretical Computer Science,* 361(2-3):210--225, 2006.
(Link to TCS
here.)

* Semidefinite approximations for global unconstrained polynomial optimization.*
With Dorina Jibetean.
* SIAM Journal on Optimization* 16(2) 490--514, 2005.
File.

Semidefinite bounds for the stability number of a graph via sums of squares of polynomials.
With N. Gvozdenovic.
Mathematical Programming, 110(1):145--173, 2007.
(Extended abstract in Lecture Notes in Computer Science, vol 3509/2005,
pages 136-151.
* Integer Programming and Combinatorial Optimization: 11th International
IPCO
Conference, *
Berlin, June 8-10, 2005.)

*On the equivalence of algebraic approaches to the minimization of forms on the simplex. *
With E. de Klerk and P. Parrilo. In * Positive Polynomials in Control,* D. Henrion and A. Garulli, eds.,
Lecture Notes on Control and Information Sciences, Vol. 312, pages 121-133, Springer Verlag, Berlin, 2005.
Paper
here.

Revisiting two theorems of Curto and Fialkow
on moment matrices.
Proceedings of the American Mathematical Society 133, no. 10, 2965-2976, 2005.

Semidefinite relaxations for Max-Cut.
In The Sharpest Cut: The Impact of Manfred Padberg and His Work.
M. Gr\"otschel, ed.,
pages 257-290,

Lower bound for the number of iterations
in semidefinite relaxations for the cut polytope.
Mathematics of Operations Research, 28(4):871--883, 2003.

A comparison of the Sherali-Adams, Lov\'asz-Schrijver and Lasserre relaxations for 0-1 programming.
Mathematics of Operations Research, 28(3):470-496, 2003.

Tighter linear and semidefinite relaxations for max-cut based on the
Lov\'asz-Schrijver lift-and-project procedure.
SIAM Journal on Optimization, 12:345--375, 2001.

* Connections between semidefinite relaxations of the max-cut and
stable set problems*
(with S. Poljak and F. Rendl).
Mathematical Programming, 77:225-246, 1997.

* On the facial structure of the set of correlation matrices*
(with S. Poljak).
SIAM Journal on Matrix Analysis, 17:530--547, 1996.

* Gap inequalities for the cut polytope *
(with S. Poljak). European Journal of Combinatorics,
17:233--254, 1996.

* On a positive semidefinite relaxation of the cut polytope
*
(with S. Poljak).
Linear Algebra and its Applications, 223/224:439--461, 1995.

** Matrix completion **

* On the sparsity order of a graph and its deficiency in chordality. *
Combinatorica, 21:543-570, 2001.

* Polynomial instances of the positive
semidefinite and euclidean distance matrix completion problems. *
SIAM Journal on Matrix Analysis and its Applications, 22:874-894, 2000.

* A connection between positive semidefinite
and Euclidean distance matrix completion problems.*
Linear Algebra and its Applications, 273:9--22, 1998.

* Cuts, matrix completions and graph rigidity.*
Mathematical Programming, 79:255--283, 1997.

* The real positive semidefinite completion problem for series-parallel
graphs.*
Linear Algebra and its Applications, 252:347--366, 1997.

** Metric spaces (the equidistant problem) **

* Equilateral dimension of the rectilinear space. *
With J. Koolen and A. Schrijver.
Designs, Codes and Cryptography, 21, 149--164, 2000.

* Embedding into rectilinear spaces *
(with H.-J. Bandelt and V. Chepoi).
Discrete and Computational Geometry, 19:595--604, 1998.

** Cycles in binary matroids **

*
Cycle bases for lattices of binary matroids with no Fano dual
minor and their one-element extensions.*
With T. Fleiner, W. Hochst\"attler and M. Loebl.
Journal of Combinatorial Theory B 77:25--38, 1999.

* A characterization of box $1/d$-integral binary clutters*
(with A.M.H. Gerards).
Journal of Combinatorial Theory B, 65:186--207, 1995.

** Graph parameters **

* A minor-monotone graph invariant based on oriented matroids
*
(with J. Edmonds and A. Schrijver). Discrete Mathematics,
165/166:219--226, 1997.

* On a minor-monotone graph invariant*
(with H. van der Holst and A. Schrijver).
Journal of Combinatorial Theory B, 65:291--304, 1995.

** Hypermetric spaces and geometry of numbers **

* Delaunay transformations of Delaunay polytopes. *
Journal of Algebraic Combinatorics, 5:37--46, 1996.

* Hypermetrics in geometry of numbers*
(with M. Deza and V.P. Grishukhin).
In L. Lov\'asz W. Cook and P. Seymour, editors, Combinatorial
Optimization, volume 20 of DIMACS Series in Discrete Mathematics and
Theoretical Computer Science. American Mathematical Society,
pages 1--109, 1995.

* The hypermetric cone is polyhedral*
(with M. Deza and V.P. Grishukhin).
Combinatorica, 13:1--15, 1993.

* Extreme hypermetrics and $L$-polytopes*
(with M. Deza and V.P. Grishukhin).
In G. Halasz et al., editor, Sets, Graphs and Numbers,
volume 60 of Colloquia Mathematica Societatis Janos Bolyai, pages
157--209, 1992.

Semidefinite programming characterization and computation of real radical ideals at *
MEGA*, Stockholm, May 30-June 3, 2011.

Optimization over polynomials with sums of squares and moment matrices
at * Positivity, Valuations and Quadratic Forms*,
Konstanz, October 1-6, 2009.

Computing real radical ideals and real
roots of polynomial equations with
semidefinite programming
at *
Convex Algebraic geometry, Optimization, and Applications*,
AIM, Palo Alto, September 21-25, 2009.

Semidefinite programming bounds for stable sets and coloring at * Combinatorial Optimization*, Oberwolfach, November 10-14, 2008.

Real solving polynomial equations with semidefinite programming at LAW 2008,
Kranjska Gora, Slovenia, May 27-June 5, 2008.

Three lectures on * Moment Matrices and Optimization over Polynomials *
as part of the
**ADONET Doctoral school on Optimization over Polynomials and Semidefinite Programming **
organized at the University of Klagenfurt, September 12-16, 2005.

1. Moment Matrices and Optimization over Polynomials - General Introduction

2. Algebraic Preliminaries and Results about Moment Matrices

3. Unconstrained Polynomial Optimization

Lecture on Semidefinite Programming in Polynomial Optimization at the SIAM Conference on Optimization, Stockholm, May 15-19, 2005. (More compact set of slides here.)

Five lectures on

September 1-12, 2003.

1. A Journey from some classic polyhedral results to the Goemans-Williamson approximation algorithm for Max-Cut.

2. The maximum stable set problem: Basic polyhedral results and the Theta function.

3. Lift-and-Project methods for 0/1 programming.

4. Polynomial optimization and sums of squares of polynomials.

5. Approximating the stability number of a graph via copositive programming - Approximating forms over the simplex - Polya's theorem.

Conference Geometric Convex Combinatorics, Oberwolfach, 16-22 June, 2002. Semidefinite relaxations for 0-1 polytopes - Application to Max-Cut.

Conference HPOPT, Utrecht, 6-8 June 2001. Cut, lift, and project methods for 0-1 programming.

Associate editor,
SIAM Journal on Optimization (SIOPT) (2001-2015).

Associate editor,
Mathematics of Operations Research (2001-2013).

Associate editor,
SIAM Journal on Discrete Mathematics (SIDMA) (2007-2019).

Associate editor,
Mathematical Programming, Series A
(since 2012).

Associate editor,
SIAM Journal on Mathematics of Data Science (SIMODS)
(2018-2022).

Editor,
Indagationes Mathematicae, since 2018.

Associate editor,
Journal of Mathematical Analysis and its Applications
(2006-2009).

Editorial board of the MPS-SIAM book
Series on Optimization (2003-2007).

Research Semester Programme
on ** Polynomial Optimization and Applications** at CWI in fall 2022, including the following events:
Workshop on Semidefinite and Polynomial Optimization on 28 August-2 September 2022,
Workshop on Solving Polynomial Equations and Applications on 5-7 October 2022,
Workshop on Polynomial Optimization and Applications in Control and Energy on 17-18 November 2022.

Geometry and Optimization in Quantum Information, Oberwolfach workshop, October 3-9, 2021.

** [cancelled]** 7th SDP Day, CWI Amsterdam, May 6, 2020.

CWI-Inria International Lab Workshop 2018, Inria, Paris, 26-26 September 2018.

6th SDP Day, CWI, Amsterdam, 5 April, 2018.

5th SDP Day, CWI, June 30, 2016.

Semidefinite Programming and Graph Algorithms, ICERM, Brown University, February 10-14, 2014.

4th SDP Days, CWI, Amsterdam, March 21, 22, 2013.

Thematic programme on Polynomial Optimisation at the Isaac Newton Institute for Mathematical Sciences, Cambridge UK, 15 July - 9 August 2013.

Workshop on
**
Geometry and Algebra of Linear Matrix Inequalities**,
Centre International de Rencontres Mathematiques (CIRM), November 12-16, 2013.

Thematic programme **
Inverse Moment Problems: the Crossroads of Analysis, Algebra, Discrete Geometry and Combinatorics**, IMS-NUS, Singapore, November 2013 - January 2014.

MFO Workshop on
Combinatorial Optimization, Oberwolfach, November 14--19, 2011.

CWI Workshop Day on
Applications of Semidefinite Programming,
July 1, 2011.

Additional lectures on Thursday June 30.

CWI Symposium Day on
Large-Scale and Uncertain Optimization,
November 12, 2010.

IPAM trimester program:
** Modern Trends in Optimization and Its Application**, UCLA,
September 13-December 17, 2010.

** Oberwolfach seminar** on
Semidefinite Optimization: Theory, Algorithms and Applications,
Oberwolfach, May 23-29, 2010. With lectures by S. Arora, M. Laurent, P. Parrilo, F. Rendl and F. Vallentin. Details can be found
here.

** EIDMA minicourse** on
Algebraic Optimization and Semidefinite Programming by Prof. Pablo Parrilo (MIT), CWI, May 31 - June 4, 2010. Registration is open till May 6, 2010. Details about the venue at CWI here.

** HPOPT 2010** -
11th International Workshop on High Performance Optimization Techniques -
Advances in Semidefinite Programming, University of Tilburg,
June 14 - 16, 2010.

CWI seminar day, **
Applications of semidefinite programming**, CWI, Amsterdam, December 3, 2009.

Oberwolfach seminar,
**New Trends in Algorithms for Real Algebraic Geometry**, MFO, Oberwolfach,
November 22-28, 2009. With lectures by S. Basu, M. Laurent, M.-F. Roy, and F. Sottile.

Oberwolfach Seminar:
** New Trends in Algorithms for Real Algebraic Geometry**,
MFO, Oberwolfach, November 22-28, 2009.

DIAMANT seminar day:
** Applications of semidefinite programming**, CWI, Amsterdam, March 13, 2009.

Minisymposium: ** Algebra in Optimization** at
5th ECM, Amsterdam, July 14-18, 2008.

HPOPT 2008 - 10th International Workshop on High Performance Optimization Techniques, Tilburg, June 11-13, 2008,
on
** Algebraic Structure in Semidefinite Programming**, with a tutorial day on June 11 on ** Using Symmetry in Semidefinite Programming.**

DIAMANT Intercity seminar on
** Algebra and Symmetries in Combinatorics and Optimization**,
University of Amsterdam, June 30, 2006.

ADONET Doctoral school on
** Optimization over Polynomials and Semidefinite Programming, **
University of Klagenfurt, September 12-16, 2005.

HPOPT 2004,
dedicated to the memory of Jos Sturm:
8th International Workshop on High Performance Optimization
Techniques, CWI, Amsterdam, June 23-25, 2004,
on ** Optimization and Polynomials, **
including a tutorial day on ** Sums of Squares
in Optimization. **

Research Program on Polynomial Optimization, Fall 2022. In construction.

Positivity, 7-9 November 2022, Princeton University.

ICCOPT 2022, 25-28 July 2022, Lehigh Univ.

Workshop The Christoffel-Darboux Kernel and Applications, Newcastle, 4-5 July 2022.

24th Conference of the International Linear Algebra Society (ILAS 2022), Galway, 20-24 June 2022.

International Symposium on Combinatorial Optimization (ISCO 2022), 18-20 May 2022.

Workshop `Conic Linear Optimization for Computer-Assisted Proofs', Oberwolfach, 10-16 April 2022.

POEMA Workshop 4, 7-11 February 2022, Tilburg.

SIAM Conference on Applied Algebraic Geometry, August 16-20, 2021 (online).

SIAM Conference on Optimization, July 20-23, 2021 (online).

EUROPT 2021, Toulouse 7-9 July 2021.

Workshop on Distance Geometry, Semidefinite Programming and Applications, Fields Institute (online), 10-14 May 2021. Within the Thematic Program on Geometric Constraint Systems, Framework Rigidity, and Distance Geometry, January-June 2021.

Online POEMA Workshop on foundations of polynomial optimization: 20 October, 26 November and 11 December 2020.

Online tutorial lectures on Polynomial Optimization (POEMA); weekly lectures, on Wednesday at 16h00, starting on Wednesday 27 May 2020.

Séminaire Français Optimisation , presentation on June 10 2020.

Mathematics Colloquium, Osnabruck, February 12, 2020.

POEMA 1st Workshop. Florence, 15-17 January 2020.

Analytical and combinatorial methods in quantum information theory. ICMS Edinburgh, 9-13 September 2019.

SIAM Conference on Applied Algebraic Geometry. Bern, 9--13 July 2019.

NMC 2019. Veldhoven, 23-24 April 2019.

UCD/IBM Quantum Technologies Colloquium 2019. Dublin, 28 March 2019.

KNAW Symposium Netwerken, Openbare Bibliotheek Amsterdam, 16 October 2018.

ICM 2018, Rio de Janeiro, 1-9 August 2018.

World Meeting for Women in Mathematics - (WM)^2, satellite event of ICM 2018, Rio de Janeiro, 31 July 2018.

ISMP 2018, Bordeaux, 1-6 July 2018.

Workshop Optimization: Fundamentals and Algorithms for Structured Problems, Toulouse, 28-29 June, 2018.

6th SDP Day, CWI, Amsterdam, 5 April, 2018.

54-th Dutch Mathematical Congress (NMC 2018), Veldhoven, 3-4 April 2018.

Leonid Gurvits's Day - A 60th Birthday Celebration. The City College of New York, 20 November 2017.

Special Program Bridging Continuous and Discrete Optimization at Simons Institute, Berkely, Fall 2017. In particular, workshop Hierarchies, Extended Formulations and Matrix-Analytic Techniques, November 6-9, 2017.

LAGOS 2017, CIRM Marseille, 11-15 September 2017.

FOCM 2017, Barcelona, July 10-19, 2017.

SIAM Conference on Optimization, May 22-25, 2017, Vancouver. Co-organization of mini-symposium

Real Algebraic Geometry With a View Toward Moment Problems and Optimization, MFO Oberwolfach, March 5-11, 2017.

LMS-CMI Research School on Combinatorics and Operators in Quantum Information Theory, Queen University Belfast, 5-9 September 2016.

ILAS 2016, Leuven, July 11-15 2016.

2016 Colloquia in Combinatorics, Queen Mary College and LSE, May 11-12, 2016.

Andrejewski-Tage 2016, Konstanz, April 7-9, 2016.

Journees SMAI-MODE, Toulouse, March 23-25, 2016.

MINO-COST Spring School on Optimization, Tilburg, March 10-13, 2015.

ISMP 2015, Pittsburgh, July 12-17, 2015.

n Combinatorial Optimization - HIM, special trimester program, Bonn, September 1-December 18, 2015.

Rigidity Workshop, October 5-9, 2015.

Relaxation Workshop, November 16-20, 2015.

Game Theory Workshop, December 14-17, 2015.

Workshop on Zero-error information, Operators, and Graphs, Barcelona, November 25-27, 2015.

Real Algebraic Geometry With A View Toward Systems Control and Free Positivity , MFO Oberfolfach, April 6-12, 2014.

Nederlands Mathematisch Congres 2014, Delft, April 16-17, 2014.

SIAM Conference on Optimization, San Diego, May 19-22, 2014.

ICM 2014, Seoul, August 13-21, 2014.

Workshop Emerging Developments in Real Algebraic Geometry: Positivity, Convexity, NC-Geometry, Optimization , Magdeburg, February 20-24, 2012.

Workshop HPOPT 2012: Algorithmic convexity and applications, Delft, June 20-22, 2012.

ISMP 2012: 21st International Symposium on Mathematical Programming, Berlin, August 19-24, 2012.

MAP 2012: Mathematics, Algorithms and Proofs, Konstanz, September 17--21, 2012.

Workshop on

FaLNMB course: Networks and Semidefinite Programming, from November 21 2022 to 20 February 2023, weekly ** onsite in Utrecht ** between 11h00-12h45.
Spring 2022, Mastermath course: ** Semidefinite Optimization**, on Thursday's 14h00-16h45, from 10 February to 19 May, at UU (details at Mastermath).

Fall 2020, LNMB Course: Networks and Semidefinite Programming.

Spring 2020,
Mastermath course: ** Semidefinite Optimization**, on Tuesday's 10h15-13h00, between 4 February and 19 May 2020 at VU (details at Mastermath).

Fall 2018, LNMB Course: Networks and semidefinite programming.

Spring 2018, Mastermath course Semidefinite Optimization.

Fall 2016,
LNMB PhD course - ** Networks and Semidefinite Programming**, on Monday 21/11/16 till 20/02/17, 11:00 - 12:45, at Utrecht University.
Course website
here.

** Course Discrete Mathematics** at AUC (Amsterdam University College), Fall 2015, 2016, 2017.

Spring 2016, Mastermath course on Semidefinite Optimization on Tuesdays, 10:15-13:00 at Utrecht University. Lecture Notes here.

Fall 2014,
LNMB PhD course - ** Networks and Semidefinite Programming**, on Mondays, 10:15 - 12:00, at Utrecht University, from Monday 17 November 2014 until Monday 9 February 2015. Course website
here.

Spring 2014, Mastermath course on Semidefinite Optimization on Tuesdays, 10:15-13:00, at BBL169 (Buys Ballotbuilding) in Utrecht University. (From Feb. 4 till May 13 2014.)

Fall 2012, LNMB course Networks and Semidefinite Programming on Mondays, 10h15-12h00, Utrecht University, Mathematical Building, room 611AB.

Spring 2012, Mastermath Course on Semidefinite Optimization on Tuesdays, UvA C1.112, 10h45 - 13h00.

TENORS: Tensor modEliNg, geOmetRy and optimiSation, EU Marie Sklodowska-Curie Joint Doctoral Network, 2024-2027. See the Cordis project webpage and the poster.

OPTIMAL: Optimization for and with Machine Learning, NWO ENW Groot (XL) project, May 2019-August 2025.

POEMA:
Polynomial Optimization, Efficiency Through Moments and Algebra,
EU Marie Marie Sklodowska-Curie Action Innovative Training Network, 2019-2022.

MINOA: *Mixed-Integer Non-Linear Optimisation Applications*,
EU Marie Marie Sklodowska-Curie Action Innovative Training Network,
2018-2021.

MINO,
* Initial Training Network Mixed Integer Nonlinear Optimization*,
2013-2016.

DIAMANT ,
*
Discrete, Interactive and Algorithmic Mathematics, Algebra and Number Theory
* [dutch mathematics cluster funded by NWO, OCW and EZ]

ADONET ,
*
Algorithmic Discrete Optimization Network *
[EU Marie Curie Research Training Network]

RAAG,
* Real Algebraic and Analytic Geometry Network*
[EU Research and Training Network]

Mathematical Optimization Society

List of publications on MathSciNet

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