## Periodic Reporting for period 3 - TAMING (Taming non convexity?)

Reporting period: 2018-09-01 to 2019-08-31

by other methods, e.g. in Control, Optimal Control and Robotics, in some inverse problems, in Statistics, Machine Learning. Therefore, and according to the accepted proposal TAMING, the research plan consists of mainly two types of research investigations: (I) Theoretical and algorithmic research on the moment–SOS approach, and (II) versatility and power of the moment-SOS approach."

II. APPLICATIONS OF THE MOMENT-SOS HIERARCHY: [5], [6], [7], [34], [39]. OPTIMIZATION: [8], [9], [10], [11], [12]. INVERSE PROBLEMS: [13], [20], [14], [15], [25], [21], [16], [37]. PROBABILITY: [22], [23], [40]. STATISTICS, MACHINE LEARNING, DATA ANALYSIS: [26], [18], [24], [35]. APPROXIMATION THEORY: [26], [32], [33]. NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS: [30], [31]

[1] J.B. Lasserre, Kim-Chuan Toh, S. Yang. Eur. J. Comput. Optim. 5, pp. 87–117, 2017

[2] T. Weisser, J.B. Lasserre, K. Toh. Math. Program. Comput. 9, pp. 1--32, 2017.

[3] C. Josz. On the relationship between real and complex linear systems. 2016. Submitted

[4] C. Josz. Algorithms for optimization and interpolation based on hyponormaliy. 2017. Submitted

[5] M. Korda, D. Henrion. Optim. Letters, pp. 1--8, 2017.

[6] M. Korda, D. Henrion, C. N. Jones. Systems & Control Letters 100, pp. 1--5, 2017.

[7] M. Korda, D. Henrion, C. N. Jones. Automatica 67, pp. 54--66, 2016

[8] J.B. Lasserre. SIAM J. Optimization 26, pp. 247—273, 2016.

[9] V. Jeyakumar, J.B. Lasserre, G. Li, Tien Son Pham. SIAM J. Optim., pp. 753—780, 2016.

[10] R. Hess R., D. Henrion, J.B. Lasserre, Tien Son Pham. SIAM J. Control & Optim. 54, pp. 1633—1656, 2016.

[11] F. Bugarin, D. Henrion, J.B. Lasserre. Math. Program. Comput. 8, pp. 83—111, 2016.

[12] J.B. Lasserre. Oper. Res. Letters. 44, pp. 158—164, 2016

[13] E. Pauwels, D. Henrion, J.B. Lasserre. SIAM J. Control & Optim. 54, pp. 1798—1825, 2016

[14] J.-P. Laumond, N. Mansard, J.B. Lasserre. Geometric and Numerical Foundations of Movements. Springer Tracts in Advanced Robotics, New York, 2017.

[15] Y. De Castro, F. Gamboa, D. Henrion, J.B. Lasserre. IEEE Trans. Information. Theory 63, pp. 621—630, 2017

[16] J.B. Lasserre. Adv. Comput. Math. 42, pp. 1129—1148, 2016.

[17] J.B. Lasserre. Adv. Applied Math. 91, pp. 137--163, 2017.

[18] J.B. Lasserre, E. Pauwels. Proceeding 2016 NIPS Conference, Barcelona, 2016.

[19] C. Josz, D. Molzahn. SIAM J. Optim. 28, pp. 1017--1048, 2018

[20] E. Pauwels, D. Henrion, J.B. Lasserre. J.-P. Laumond, N. Mansard and J.B. Lasserre (Eds.), Springer Tracts in Advanced Robotics 117, Springer, Switzerland, 2017, pp. 113—132.

[21] J.B. Lasserre. SIGMA 11 (077), 2015.

[22] J.B. Lasserre, Y. Emin. Math. Operations Research, doi/10.1287/moor.2018.0980

[23] J.B. Lasserre. IEEE Control Systems Letters 1, pp. 50-55, 2017.

[24] J.B. Lasserre, E. Pauwels. Adv. Comp. Math. 45, pp. 1439--1468, 2019

[25] C. Josz, J.B. Lasserre, B. Mourrain. Adv. Comp. Math. 45, pp. 1401--1437, 2019

[26] Y. De Castro, F. Gamboa, D. Henrion, R. Hess, J.B. Lasserre. The Annals of Statistics 47, pp. 127--155, 2019

[27] J. Rouot, J.B. Lasserre. Proc. 56th IEEE CDC Conference, Melbourne, December 2017.

[28] S. Foucart, J.B. Lasserre. J. Approximation Theory 235, pp. 74--91, 2018

[29] J.B. Lasserre. Proceedings ICM 2018, Rio de Janeiro.

[30] M. Korda, D. Henrion, J.B. Lasserre. arXiv:1804.07565

[31] S. Marx, T. Weisser, D. Henrion, J.B. Lasserre. Math. Control & Related Fields, 2019

[32] S. Foucart, J.B. Lasserre. Computational Methods and Function Theory. 2019

[33] S. Marx, E. Pauwels, T. Weisser, D. Henrion, J.B. Lasserre. Tractable semi-algebraic approximation using Christoffel-Darboux kernels. submitted

[34] J.B. Lasserre. SIAM J. Appl. Algebra & Geometry 3, pp. 372--389, 2019

[35] J.B. Lasserre & V. Magron. SIAM J. Optim. 28, pp. 3127--3144, 2018

[36] J.B. Lasserre & V. Magron. SIAM J. Optim. 29, pp. 2128--2145, 2019

[37] F. Bréhard, M. Joldes and J.B. Lasserre. Proceedings ISSAC'2019, Beijing, 2019, pp. 66--73.

[38] J.B. Lasserre. Submitted. arXiv:1907.09784

[39] J.B. Lasserre. European Control Conference (ECC 2019), Naples, Italy, July 2019

[40] J.B. Lasserre & T. Weisser. Math. Program Séries A. 2019

II. All contributions in II.1 -> II.5 describe a completely new methodology for difficult problems: (i) Optimal design for polynomial regression in Statistics, (ii) nonlinear hyperbolic PDE's, and (iii) the Christoffel

function for Statistics & Machine Learning should have a noticeable impact very soon. In recognition of the impact of this methodology:

•The paper [37] got the ISSAC 2019 Best Paper Award at the ISSAC 2019 conference in Beijing, July 2019.

•J.B. Lasserre was an invited speakers (with David Vogan from MIT) at the 90th Anniversary of the Department of Mathematics, National University of Singapore (NUS), September 2019.

• was invited as Simons CRM Professor at CRM in Montreal (Canada)

•was an invited speaker at the International Congress of Mathematics (ICM 2018, Rio de Janeiro)

•was invited to speak at several specialized workshop at prestigious Institutes of Mathematics

•was Keynote or plenary speaker at various conferences and workshops.

•was speaker at the prestigious Mathematical Colloquia (Charles University in Praha, Tcheky) in 2017.

•was awarded the 2015 John von Neumann Theory Prize of the INFORMS Society as well as the L. Khachiyan Prize of the Optimization Society of INFORMS (for Lifetime achievement in Optimization)

•will hold an “optimization chair” in the newly created ANITI Institute (Toulouse, France) for Artificial Intelligence.

•Didier Henrion has been invited to speak at several workshops and conferences

•Cédric Josz and Didier Henrion got (jointly) in 2016 the Optimization Letters Best Paper Award.

•Swann Marx spent the whole month of January 2019 at the Deusto University (Bilbao, Basque country) at the invitation of Enrique Zuazua