A. Antoniadis, Analysis of variance on function spaces, Math. Operationsforsch. u. Statist, vol.15, issue.1, p.5971, 1984.

P. Audze and V. Eglais, New approach for planning out of experiments. Problems of Dynamics and Strengths, vol.35, p.104107, 1977.

Y. Auray, P. Barbillon, and J. Marin, Maximin design on non hypercube domains and kernel interpolation, Statistics and Computing, vol.22, issue.3, p.703712, 2012.

F. Bach, S. Lacoste-julien, and G. Obozinski, On the equivalence between herding and conditional gradient algorithms, Proc. ICML 2012, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00681128

A. Beck and M. Teboulle, A conditional gradient method with linear rate of convergence for solving convex linear systems, Mathematical Methods of Operations Research, vol.59, issue.2, pp.235-247, 2004.

J. Bect, F. Bachoc, and D. Ginsbourger, A supermartingale approach to Gaussian process based sequential design of experiments, Bernoulli, p.2019
URL : https://hal.archives-ouvertes.fr/hal-01351088

J. Bect, D. Ginsbourger, L. Li, V. Picheny, and E. Vazquez, Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, vol.22, issue.3, p.773793, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00689580

A. Berlinet and C. Thomas-agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics. Kluwer, 2004.

S. Biedermann and H. Dette, Minimax optimal designs for nonparametric regression a further optimality property of the uniform distribution, mODa'6 Advances in ModelOriented Design and Analysis, Proceedings of the 76th Int. Workshop, Puchberg/Schneeberg (Austria), p.1320, 2001.

G. Björck, Distributions of positive mass, which maximize a certain generalized energy integral, Arkiv för Matematik, vol.3, issue.21, p.255269, 1956.

D. Böhning, Numerical estimation of a probability measure, Journal of Statistical Planning and Inference, vol.11, p.5769, 1985.

D. Böhning, A vertex-exchange-method in D-optimal design theory, Metrika, vol.33, p.337347, 1986.

A. Breger, M. Ether, and M. Gräf, Points on manifolds with asymptotically optimal covering radius, Journal of Complexity, vol.48, p.114, 2018.

F. Briol, C. Oates, M. Girolami, and M. A. Osborne, Frank-Wolfe Bayesian quadrature: Probabilistic integration with theoretical guarantees, Advances in Neural Information Processing Systems, p.11621170, 2015.

F. Briol, C. J. Oates, M. Girolami, M. A. Osborne, and D. Sejdinovic, Probabilistic integration: A role in statistical computation?, Statistical Science, vol.34, issue.1, p.122, 2019.

H. Cardot, P. Cénac, and J. Monnez, A fast and recursive algorithm for clustering large datasets, Comput. Statist. Data Anal, vol.56, issue.6, p.14341449, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00644683

W. Y. Chen, L. Mackey, J. Gorham, F. Briol, and C. J. Oates, Proc. ICML, 2018.

Y. Chen, M. Welling, and A. Smola, Super-samples from kernel herding, Proceedings 26th Conference on Uncertainty in Articial Intelligence (UAI'10), p.109116, 2010.

K. M. Clarkson, Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm, ACM Transactions on Algorithms (TALG), vol.6, issue.4, p.63, 2010.

S. B. Damelin, F. J. Hickernell, D. L. Ragozin, and X. Zeng, On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space, J. Fourier Anal. Appl, vol.16, p.813839, 2010.

G. Detommaso, T. Cui, Y. Marzouk, A. Spantini, and R. Scheichl, A Stein variational Newton method, Advances in Neural Information Processing Systems, p.91879197, 2018.

H. Dette, A. Pepelyshev, and A. Zhigljavsky, Best linear unbiased estimators in continuous time regression models, The Annals of Statistics, vol.47, issue.4, p.19281959, 2019.

P. Diaconis, Bayesian numerical analysis. Statistical Decision Theory and Related Topics IV, vol.1, p.163175, 1988.

J. Dick and F. Pillichshammer, Digital Nets and Sequences. Discrepancy Theory and QuasiMonte Carlo Integration, 2010.

Q. Du, V. Faber, and M. Gunzburger, Centroidal Voronoi tessellations: applications and algorithms, SIAM Review, vol.41, issue.4, p.637676, 1999.

J. C. Dunn, Convergence rates for conditional gradient sequences generated by implicit step length rules, SIAM J. Control and Optimization, vol.18, issue.5, p.473487, 1980.

J. C. Dunn and S. Harshbarger, Conditional gradient algorithms with open loop step size rules, Journal of Mathematical Analysis and Applications, vol.62, p.432444, 1978.

N. Durrande, D. Ginsbourger, O. Roustant, and L. Carraro, Anova kernels and RKHS of zero mean functions for model-based sensitivity analysis, Journal of Multivariate Analysis, vol.115, p.5767, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00601472

N. Durrande, J. Hensman, M. Rattray, and N. D. Lawrence, Detecting periodicities with Gaussian processes, PeerJ Comput. Sci, vol.2, p.50, 2016.
URL : https://hal.archives-ouvertes.fr/emse-01351044

K. Fang, R. Li, and A. Sudjianto, Design and Modeling for Computer Experiments. Chapman & Hall/CRC, 2006.

V. V. Fedorov, Theory of Optimal Experiments, 1972.

M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Res. Logist. Quart, vol.3, p.95110, 1956.

B. Fuglede, On the theory of potentials in locally compact spaces, Acta mathematica, vol.103, pp.139-215, 1960.

B. Fuglede and N. Zorii, Green kernels associated with Riesz kernels, Annales Academiae Scientiarum Fennicae, p.43, 2018.

B. Gauthier and L. Pronzato, Spectral approximation of the IMSE criterion for optimal designs in kernel-based interpolation models, SIAM/ASA J. Uncertainty Quantication, vol.2, pp.805-825, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00913466

B. Gauthier and L. Pronzato, Convex relaxation for IMSE optimal design in random eld models, Computational Statistics and Data Analysis, vol.113, p.375394, 2017.

D. Ginsbourger, Sequential design of computer experiments, vol.99, p.111, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00689580

D. Ginsbourger, O. Roustant, D. Schuhmacher, N. Durrande, and N. Lenz, On ANOVA decompositions of kernels and Gaussian random eld paths, Monte Carlo and Quasi-Monte Carlo Methods, p.315330, 2016.

T. Gneiting, Strictly and non-strictly positive dene functions on spheres, Bernoulli, vol.19, issue.4, p.13271349, 2013.

A. Gorodetsky and Y. Marzouk, Mercer kernels and integrated variance experimental design: connections between Gaussian process regression and polynomial approximation, SIAM/ASA J. Uncertainty Quantication, vol.4, issue.1, p.796828, 2016.

S. Graf and H. Luschgy, Foundations of Quantization for Probability Distributions, 2000.

U. Grenander, Stochastic processes and statistical inference, Arkiv för Matematik, vol.1, issue.3, pp.195-277, 1950.

D. P. Hardin and E. B. Sa, Discretizing manifolds via minimum energy points, Notices of the AMS, vol.51, issue.10, p.11861194, 2004.

P. Hennig, M. A. Osborne, and M. Girolami, Probabilistic numerics and uncertainty in computations, Proc. Royal Soc. A, vol.471, p.20150142, 2015.
DOI : 10.1098/rspa.2015.0142
URL : http://europepmc.org/articles/pmc4528661?pdf=render

J. Hensman, N. Durrande, and A. Solin, Variational Fourier features for Gaussian processes, Journal of Machine Learning Research, vol.18, p.152, 2018.
URL : https://hal.archives-ouvertes.fr/emse-01411206

F. J. Hickernell, A generalized discrepancy and quadrature error bound. Mathematics of Computation, vol.67, p.299322, 1998.
DOI : 10.1090/s0025-5718-98-00894-1
URL : https://www.ams.org/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf

F. Huszár and D. Duvenaud, Optimally-weighted herding is Bayesian quadrature, Proceedings 28th Conference on Uncertainty in Articial Intelligence (UAI'12), pp.377-385, 2012.

M. E. Johnson, L. M. Moore, and D. Ylvisaker, Minimax and maximin distance designs, Journal of Statistical Planning and Inference, vol.26, p.131148, 1990.
DOI : 10.1016/0378-3758(90)90122-b

V. R. Joseph, T. Dasgupta, R. Tuo, and C. F. Wu, Sequential exploration of complex surfaces using minimum energy designs, Technometrics, vol.57, issue.1, p.6474, 2015.

V. R. Joseph, E. Gul, and S. Ba, Maximum projection designs for computer experiments, Biometrika, vol.102, issue.2, p.371380, 2015.
DOI : 10.1093/biomet/asv002

T. Karvonen, C. J. Oates, and S. Särkkä, A Bayes-Sard cubature method, Advances in Neural Information Processing Systems, p.58865897, 2018.

T. Karvonen and S. Särkkä, Classical quadrature rules via Gaussian processes, 27th IEEE International Workshop on Machine Learning for Signal Processing (MLSP), p.16, 2017.
DOI : 10.1109/mlsp.2017.8168195
URL : https://research.aalto.fi/files/15931102/KarvonenSarkka2017_MLSP.pdf

J. Kiefer and J. Wolfowitz, Optimum designs in regression problems, Annals of Math. Stat, vol.30, p.271294, 1959.

N. M. Korobov, Properties and calculation of optimal coecients, Doklady Akademii Nauk SSSR, vol.132, issue.5, p.10091012, 1960.

N. S. Landkof, Foundations of Modern Potential Theory, 1972.

F. M. Larkin, Gaussian measure in Hilbert space and applications in numerical analysis, The Rocky Mountain Journal of Mathematics, vol.2, issue.3, p.379421, 1972.

F. M. Larkin, Probabilistic error estimates in spline interpolation and quadrature, IFIP Congress, p.605609, 1974.

R. Lekivetz and B. Jones, Fast exible space-lling designs for nonrectangular regions, Quality and Reliability Engineering International, vol.31, issue.5, p.829837, 2015.

Q. Liu and D. Wang, Stein variational gradient descent: a general purpose Bayesian inference algorithm, Advances In Neural Information Processing Systems, p.23782386, 2016.

H. Luschgy and G. Pagès, Greedy vector quantization, Journal of Approximation Theory, vol.198, p.111131, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01026116

S. Mak and V. R. Joseph, Projected support points, with application to optimal MCMC reduction, 2017.

S. Mak and V. R. Joseph, Minimax and minimax projection designs using clustering, Journal of Computational and Graphical Statistics, vol.27, issue.1, p.166178, 2018.
DOI : 10.1080/10618600.2017.1302881
URL : http://arxiv.org/pdf/1602.03938

S. Mak and V. R. Joseph, Support points, Annals of Statistics, vol.46, issue.6A, p.25622592, 2018.
DOI : 10.1214/17-aos1629

J. Matousek, On the L2-discrepancy for anchored boxes, Journal of Complexity, vol.14, issue.4, p.527556, 1998.

I. Molchanov and S. Zuyev, Variational calculus in the space of measures and optimal design, p.7990, 2000.

I. Molchanov and S. Zuyev, Steepest descent algorithm in a space of measures, Statistics and Computing, vol.12, p.115123, 2002.

W. Näther, Eective Observation of Random Fields, Teubner-Texte zur Mathematik, vol.72, 1985.

H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, 1992.

C. J. Oates, A. Barp, and M. Girolami, Posterior integration on a Riemannian manifold, 2018.

C. J. Oates, M. Girolami, and N. Chopin, Control functionals for Monte Carlo integration, Journal of Royal Statistical Society, vol.79, issue.3, p.695718, 2017.
DOI : 10.1111/rssb.12185
URL : http://arxiv.org/pdf/1410.2392.pdf

A. O'hagan, Bayes-Hermite quadrature, Journal of Statistical Planning and Inference, vol.29, issue.3, p.245260, 1991.

V. I. Paulsen, An introduction to the theory of reproducing kernel Hilbert spaces, 2009.

L. Pronzato, Minimax and maximin space-lling designs: some properties and methods for construction, Journal de la Société Française de Statistique, vol.158, issue.1, p.736, 2017.

L. Pronzato and A. Pázman, Asymptotic Normality, Optimality Criteria and Small-Sample Properties, LNS, vol.212, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00879984

L. Pronzato, H. P. Wynn, and A. Zhigljavsky, Extremal measures maximizing functionals based on simplicial volumes, Statistical Papers, vol.57, issue.4, p.1308116, 2016.
DOI : 10.1007/s00362-016-0767-6
URL : https://hal.archives-ouvertes.fr/hal-01308116

L. Pronzato and A. A. Zhigljavsky, Algorithmic construction of optimal designs on compact sets for concave and dierentiable criteria, Journal of Statistical Planning and Inference, vol.154, p.141155, 2014.

L. Pronzato and A. A. Zhigljavsky, Measures minimizing regularized dispersion, J. Scientic Computing, vol.78, issue.3, p.15501570, 2019.
DOI : 10.1007/s10915-018-0817-4
URL : https://hal.archives-ouvertes.fr/hal-01864088

C. R. Rao, Diversity and dissimilarity coecients: a unied approach, Theoret. Popn Biol, vol.21, issue.1, p.2443, 1982.
DOI : 10.1016/0040-5809(82)90004-1

C. R. Rao and T. K. Nayak, Cross entropy, dissimilarity measures and characterizations of quadratic entropy, IEEE Transactions on Information Theory, vol.31, issue.5, p.589593, 1985.

K. Ritter, G. W. Wasilkowski, and H. Wo¹niakowski, Multivariate integration and approximation for random elds satisfying Sacks-Ylvisaker conditions, The Annals of Applied Probability, vol.5, issue.2, p.518540, 1995.
DOI : 10.1214/aoap/1177004776
URL : https://doi.org/10.1214/aoap/1177004776

J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Design and analysis of computer experiments, Statistical Science, vol.4, issue.4, p.409435, 1989.

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments, 2003.

R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics, vol.3, issue.3, p.251264, 1995.

R. Schaback, Native Hilbert spaces for radial basis functions I, New Developments in Approximation Theory, p.255282, 1999.

I. J. Schoenberg, Metric spaces and positive denite functions, Transactions of the American Mathematical Society, vol.44, issue.3, p.522536, 1938.

S. Sejdinovic, B. Sriperumbudur, A. Gretton, and K. Fukumizu, Equivalence of distance-based and RKHS-based statistics in hypothesis testing, The Annals of Statistics, vol.41, issue.5, pp.2263-2291, 2013.

B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G. R. Lanckriet, Hilbert space embeddings and metrics on probability measures, Journal of Machine Learning Research, vol.11, p.15171561, 2010.

M. L. Stein, Interpolation of Spatial Data. Some Theory for Kriging, 1999.

I. Steinwart, D. Hush, and C. Scovel, An explicit description of the reproducing kernel Hilbert spaces of Gaussian RBF kernels, IEEE Transactions on Information Theory, vol.52, issue.10, pp.4635-4643, 2006.

Z. Szabó and B. Sriperumbudur, Characteristic and universal tensor product kernels, Journal of Machine Learning Research, vol.18, p.129, 2018.

G. J. Székely and M. L. Rizzo, Energy statistics: A class of statistics based on distances, Journal of Statistical Planning and Inference, vol.143, issue.8, p.12491272, 2013.

E. Vazquez and J. Bect, Sequential search based on kriging: convergence analysis of some algorithms, Proc. 58th World Statistics Congress of the ISI, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643159

H. Wackernagel, Multivariate Geostatistics. An Introduction with Applications, 1998.

H. P. Wynn, The sequential generation of D-optimum experimental designs, Annals of Math. Stat, vol.41, p.16551664, 1970.