J. Affleck-graves, A. H. Money, and C. G. Troskie, A principal component index subject to constraints, Investment Analysts Journal, 1979.

J. Aitchison, The statistical analysis of compositional data, Journal of the Royal Statistical Society. Series B (Methodological ), vol.44, issue.2, pp.139-177, 1982.
DOI : 10.1007/978-94-009-4109-0

B. Ankenman, L. Barry, J. Nelson, and . Staum, Stochastic Kriging for Simulation Metamodeling, Operations Research, vol.58, issue.2, pp.371-382, 2010.
DOI : 10.1287/opre.1090.0754
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.642.9078

M. Bebendorf, Y. Maday, and B. Stamm, Comparison of some reduced representation approximations. arXiv preprint, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00825315

H. Richard, P. Byrd, J. Lu, C. Nocedal, and . Zhu, A limited memory algorithm for bound constrained optimization, SIAM Journal on Scientific Computing, vol.16, issue.5, pp.1190-1208, 1995.

C. Nguyen-ngoc, Reduced-basis approximations and a posteriori error bound for nonaffine and nonlinear partial differential equations: Application to inverse analysis, 2005.

S. Da, V. , and A. Marrel, Gaussian process modeling with inequality constraints, Annales de la faculté des sciences de Toulouse Mathématiques, pp.529-555

P. Delicado, Dimensionality reduction when data are density functions, Computational Statistics & Data Analysis, vol.55, issue.1, pp.401-420, 2011.
DOI : 10.1016/j.csda.2010.05.008

K. Fessart and J. Lonchampt, Optimisation d'un programme d'investissements : méthode IPOP. Conférence lambdamu, 2010.

D. Goldfarb and A. Idnani, A numerically stable dual method for solving strictly convex quadratic programs, Mathematical Programming, vol.27, issue.1, pp.1-33, 1983.
DOI : 10.1007/BF02591962

W. Hardle and J. Stephen-marron, Optimal bandwidth selection in nonparametric regression function estimation. The Annals of Statistics, pp.1465-1481, 1985.
DOI : 10.1214/aos/1176349748

J. Trevor, . Hastie, J. Robert, and . Tibshirani, Generalized Additive Models, 1990.

B. Iooss and M. Ribatet, Global sensitivity analysis of computer models with functional inputs, Reliability Engineering & System Safety, vol.94, issue.7, pp.1194-1204, 2009.
DOI : 10.1016/j.ress.2008.09.010
URL : https://hal.archives-ouvertes.fr/hal-00243156

A. Kneip and K. J. Utikal, Inference for Density Families Using Functional Principal Component Analysis, Journal of the American Statistical Association, vol.96, issue.454, pp.519-542, 2001.
DOI : 10.1198/016214501753168235

J. Lonchampt and K. Fessart, An optimization approach for life cycle management applied to large power transformers

Y. Maday, N. C. Nguyen, T. Anthony, . Patera, S. George et al., A general multipurpose interpolation procedure: the magic points, Proceedings of the 2nd International Conference on Scientific Computing and Partial Differential Equations, 2007.
DOI : 10.3934/cpaa.2009.8.383
URL : https://hal.archives-ouvertes.fr/hal-00174797

A. Marrel, B. Iooss, S. Da-veiga, and M. Ribatet, Global sensitivity analysis of stochastic computer models with joint metamodels, Statistics and Computing, vol.44, issue.1, pp.833-847, 2012.
DOI : 10.1007/s11222-011-9274-8
URL : https://hal.archives-ouvertes.fr/hal-00232805

D. Michael, . Mckay, J. Richard, . Beckman, J. William et al., Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

H. Muller and U. Stadtmuller, Variable bandwidth kernel estimators of regression curves. The Annals of Statistics, pp.182-201, 1987.

A. Elizbar and . Nadaraya, On estimating regression. Theory of Probability & Its Applications, pp.141-142, 1964.

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

J. O. Ramsay, B. W. Silverman, C. Audet, and J. E. Dennis-jr, Functional Data Analysis. Springer Series in Statistics, Biometrical Journal, vol.40, issue.1
DOI : 10.1002/(SICI)1521-4036(199804)40:1<56::AID-BIMJ56>3.0.CO;2-#

C. Audet and J. E. Dennis-jr, Analysis of Generalized Pattern Searches, SIAM Journal on Optimization, vol.13, issue.3, pp.889-903, 2002.
DOI : 10.1137/S1052623400378742

C. Bogani, M. G. Gasparo, and A. Papini, Generating Set Search Methods for Piecewise Smooth Problems, SIAM Journal on Optimization, vol.20, issue.1, pp.321-335, 2009.
DOI : 10.1137/070708032

J. Borggaard, D. Pelletier, and K. Vugrin, On Sensitivity Analysis for Problems with Numerical Noise, 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 2002.
DOI : 10.2514/6.2002-5553

D. M. Bortz and C. T. Kelley, The Simplex Gradient and Noisy Optimization Problems, of Progress in Systems and Control Theory, pp.77-90, 1998.
DOI : 10.1007/978-1-4612-1780-0_5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.7974

R. G. Carter, On the Global Convergence of Trust Region Algorithms Using Inexact Gradient Information, SIAM Journal on Numerical Analysis, vol.28, issue.1, pp.251-265, 1991.
DOI : 10.1137/0728014

R. G. Carter, Numerical Experience with a Class of Algorithms for Nonlinear Optimization Using Inexact Function and Gradient Information, SIAM Journal on Scientific Computing, vol.14, issue.2, 1993.
DOI : 10.1137/0914023

T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering, SIAM Journal on Optimization, vol.10, issue.4, pp.1149-1162, 2000.
DOI : 10.1137/S1052623499354096
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9281

A. R. Conn, K. Scheinberg, and L. N. Vicente, Introduction to Derivative-Free Optimization, MPS- SIAM Series on Optimization. SIAM, 2009.
DOI : 10.1137/1.9780898718768

A. R. Conn and L. N. Vicente, Bilevel derivative-free optimization and its application to robust optimization, Optimization Methods and Software, vol.27, issue.3, pp.561-577, 2012.
DOI : 10.1007/978-1-4615-6305-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.414.2327

C. Davis, Theory of Positive Linear Dependence, American Journal of Mathematics, vol.76, issue.4, pp.733-746, 1954.
DOI : 10.2307/2372648

O. Devolder, F. Glineur, and Y. Nesterov, First-order methods of smooth convex optimization with inexact oracle, Mathematical Programming, vol.110, issue.3, pp.37-75, 2014.
DOI : 10.1007/s10107-013-0677-5

M. Dodangeh and L. N. Vicente, Worst case complexity of direct search under convexity, Mathematical Programming, vol.1, issue.1-2
DOI : 10.1007/s10107-014-0847-0

T. Glad and A. Goldstein, Optimization of functions whose values are subject to small errors, BIT, vol.12, issue.2, pp.160-169, 1977.
DOI : 10.1007/BF01932287

S. Gratton, C. W. Royer, L. N. Vicente, and Z. Zhang, Direct Search Based on Probabilistic Descent, SIAM Journal on Optimization, vol.25, issue.3, pp.1515-1541, 2015.
DOI : 10.1137/140961602

M. Heinkenschloss and L. N. Vicente, Analysis of Inexact Trust-Region SQP Algorithms, SIAM Journal on Optimization, vol.12, issue.2, pp.283-302, 2002.
DOI : 10.1137/S1052623499361543

N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 2002.
DOI : 10.1137/1.9780898718027

C. T. Kelley, Iterative Methods for Optimization, Frontiers in Applied Mathematics. SIAM, vol.18, 1999.
DOI : 10.1137/1.9781611970920

T. G. Kolda, R. M. Lewis, and V. Torczon, Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods, SIAM Review, vol.45, issue.3, pp.385-482, 2003.
DOI : 10.1137/S003614450242889
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.5262

S. and L. Digabel, Algorithm 909, ACM Transactions on Mathematical Software, vol.37, issue.4, pp.44-45, 2011.
DOI : 10.1145/1916461.1916468

S. Lucidi and M. Sciandrone, On the Global Convergence of Derivative-Free Methods for Unconstrained Optimization, SIAM Journal on Optimization, vol.13, issue.1, pp.97-116, 2002.
DOI : 10.1137/S1052623497330392

J. J. Moré, Recent Developments in Algorithms and Software for Trust Region Methods, Mathematical Programming: The State of Art, 1983.
DOI : 10.1007/978-3-642-68874-4_11

J. J. Moré and S. M. Wild, Benchmarking Derivative-Free Optimization Algorithms, SIAM Journal on Optimization, vol.20, issue.1, pp.172-191, 2009.
DOI : 10.1137/080724083

A. Nedi´cnedi´c and D. P. Bertsekas, The effect of deterministic noise in subgradient methods, Mathematical Programming, vol.56, issue.10, pp.75-99, 2010.
DOI : 10.1007/s10107-008-0262-5

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-313, 1965.
DOI : 10.1093/comjnl/7.4.308

B. T. Polyak, Nonlinear programming methods in the presence of noise, Mathematical Programming, vol.8, issue.1, pp.87-97, 1978.
DOI : 10.1007/BF01588952

M. J. Powell, A view of algorithms for optimization without derivatives, 2007.

M. V. Solodov and S. K. Zavriev, Error Stability Properties of Generalized Gradient-Type Algorithms, Journal of Optimization Theory and Applications, vol.7, issue.3, pp.663-680, 1998.
DOI : 10.1023/A:1022680114518

. L. Ph and . Toint, Global convergence of aa of trust-region methods for nonconvex minimization in hilbert space, IMA J. Numer. Anal, vol.8, pp.231-252, 1988.

V. Torczon, On the Convergence of Pattern Search Algorithms, SIAM Journal on Optimization, vol.7, issue.1, pp.1-25, 1997.
DOI : 10.1137/S1052623493250780

L. N. Vicente, Worst case complexity of direct search, EURO Journal on Computational Optimization, vol.133, issue.1-2, pp.143-153, 2013.
DOI : 10.1007/s13675-012-0003-7

L. N. Vicente and A. L. Custódio, Analysis of direct searches for discontinuous functions, Mathematical Programming, vol.7, issue.1-2, pp.299-325, 2012.
DOI : 10.1007/s10107-010-0429-8

K. Vugrin, On the effect of numerical noise in simulation-based optimization, 2003.

M. H. Wright, Direct search methods: Once scorned, now respectable, Pitman Research Notes in Mathematics Series, vol.344, pp.191-208, 1995.

R. E. Bellman and L. A. Zadeh, Decision-Making in a Fuzzy Environment, Management Science, vol.17, issue.4, p.141, 1970.
DOI : 10.1287/mnsc.17.4.B141

G. Bortolan and R. Degani, A review of some methods for ranking fuzzy subsets. Fuzzy sets and Systems, pp.1-19, 1985.

L. Campos and J. Verdegay, Linear programming problems and ranking of fuzzy numbers. Fuzzy sets and systems, pp.1-11, 1989.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, vol.6, issue.2, pp.182-197, 2002.
DOI : 10.1109/4235.996017

S. Dempe and A. Ruziyeva, On the calculation of a membership function for the solution of a fuzzy linear optimization problem, Fuzzy Sets and Systems, vol.188, issue.1, pp.58-67, 2012.
DOI : 10.1016/j.fss.2011.07.014

D. J. Dubois, Fuzzy sets and systems: theory and applications, 1980.

M. Ehrgott, Multicriteria optimization, 2006.
DOI : 10.1007/978-3-662-22199-0

P. Grzegorzewski, Nearest interval approximation of a fuzzy number. Fuzzy Sets and systems, pp.321-330, 2002.

M. Hanss, Applied fuzzy arithmetic, 2005.

S. Liu, Quadratic programming with fuzzy parameters: A membership function approach, Chaos, Solitons & Fractals, vol.40, issue.1, pp.237-245, 2009.
DOI : 10.1016/j.chaos.2007.07.054

M. Luhandjula, Fuzzy optimization: Milestones and perspectives. Fuzzy Sets and Systems, 2014.
DOI : 10.1016/j.fss.2014.01.004

M. K. Luhandjula and M. J. Rangoaga, An approach for solving a fuzzy multiobjective programming problem, European Journal of Operational Research, vol.232, issue.2, pp.249-255, 2014.
DOI : 10.1016/j.ejor.2013.05.040

S. Nasseri, Fuzzy nonlinear optimization, The Journal of Nonlinear Sciences and its Applications, vol.1, issue.4, pp.230-235, 2008.

S. Orlovski, Mathematical programming problems with fuzzy parameters. Management decision support systems using fuzzy sets and possibility theory, pp.136-145, 1985.

H. Rommelfanger, R. Hanuscheck, and J. Wolf, Linear programming with fuzzy objectives. Fuzzy sets and systems, pp.31-48, 1989.
DOI : 10.1016/0165-0114(89)90134-6

H. Rommelfanger and R. Ss-lowi´nskilowi´nski, Fuzzy linear programming with single or multiple objective functions. In Fuzzy sets in decision analysis, operations research and statistics, pp.179-213, 1998.
DOI : 10.1007/978-1-4615-5645-9_6

H. J. Rommelfanger, Fuzzy linear programming and applications, European Journal of Operational Research, vol.92, issue.3, pp.512-527, 1996.
DOI : 10.1016/0377-2217(95)00008-9

M. Sakawa and H. Yano, Feasibility and pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, pp.1-15, 1991.
DOI : 10.1016/0165-0114(91)90017-k

H. Tanaka and K. Asai, Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and systems, pp.1-10, 1984.
DOI : 10.1016/0165-0114(84)90022-8

H. Tanaka, T. Okuda, and K. Asai, On fuzzy-mathematical programming, 1973.

L. Zadeh, Fuzzy sets, Information and Control, vol.8, issue.3, pp.338-353, 1965.
DOI : 10.1016/S0019-9958(65)90241-X

L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, vol.1, issue.1, pp.3-28, 1978.
DOI : 10.1016/0165-0114(78)90029-5

H. Zimmermann, Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, pp.45-55, 1978.
DOI : 10.1016/0165-0114(78)90031-3

H. Zimmermann, Fuzzy set theory and its applications, 2001.

J. E. Bibliographie1-]-aarnes, T. Gimse, and K. Lie, An introduction to the numerics of flow in porous media using matlab, Geometric Modelling, Numerical Simulation, and Optimization, pp.265-306, 2007.

E. Ammar and H. Khalifa, Fuzzy portfolio optimization a quadratic programming approach, Chaos, Solitons & Fractals, vol.18, issue.5, pp.1045-1054, 2003.
DOI : 10.1016/S0960-0779(03)00071-7

B. Ankenman, B. L. Nelson, and J. Staum, Stochastic Kriging for Simulation Metamodeling, Operations Research, vol.58, issue.2, pp.371-382, 2010.
DOI : 10.1287/opre.1090.0754
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.642.9078

K. Asai, H. Tanaka, and T. Okuda, Decision making and its goal in a fuzzy environment . Fuzzy sets and their applications to cognitive and decision processes, pp.257-277, 1975.

B. Auder, Classification et modélisation de sorties fonctionnelles de codes de calcul : application aux calculs thermo-hydrauliques accidentels dans les réacteurs à eau pressurisés (REP), 2011.

C. J. Bélisle, H. E. Romeijn, and R. L. Smith, Hit-and-Run Algorithms for Generating Multivariate Distributions, Mathematics of Operations Research, vol.18, issue.2, pp.255-266, 1993.
DOI : 10.1287/moor.18.2.255

R. E. Bellman and L. A. Zadeh, Decision-Making in a Fuzzy Environment, Management Science, vol.17, issue.4, p.141, 1970.
DOI : 10.1287/mnsc.17.4.B141

H. Beyer and B. Sendhoff, Robust optimization ? a comprehensive survey Computer methods in applied mechanics and engineering 196, pp.3190-3218, 2007.

A. K. Bhurjee and G. Panda, Efficient solution of interval optimization problem, Mathematical Methods of Operations Research, vol.144, issue.3, pp.273-288, 2012.
DOI : 10.1007/s00186-012-0399-0

G. Bortolan and R. Degani, A review of some methods for ranking fuzzy subsets. Fuzzy sets and Systems, pp.1-19, 1985.

N. Bousquet, Accelerated Monte Carlo estimation of exceedance probabilities under monotonicity constraints, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.21, issue.3, pp.21-557, 2012.
DOI : 10.5802/afst.1345
URL : https://hal.archives-ouvertes.fr/hal-01101250

Z. Bouzarkouna, Well placement optimization, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00690456

Z. Bouzarkouna, D. Y. Ding, and A. Auger, Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models, Computational Geosciences, vol.13, issue.4, pp.75-92, 2012.
DOI : 10.1007/s10596-011-9254-2
URL : https://hal.archives-ouvertes.fr/hal-00628126

T. Browne, Développement d'émulateur de codes stochastiques pour la résolution de problèmes d'optimisation robuste par algorithmes génétiques, 2014.

T. Browne, B. Iooss, L. L. Gratiet, and J. Lonchampt, Stochastic simulators based optimization by gaussian process metamodels-application to maintenance investments planning issues. arXiv preprint, 2015.
DOI : 10.1002/qre.2028
URL : https://hal.archives-ouvertes.fr/hal-01198463

L. Campos and J. Verdegay, Linear programming problems and ranking of fuzzy numbers. Fuzzy sets and systems, pp.1-11, 1989.
DOI : 10.1016/0165-0114(89)90084-5

E. Canestrelli, S. Giove, and R. Fullér, Stability in possibilistic quadratic programming, Fuzzy Sets and Systems, vol.82, issue.1, pp.51-56, 1996.
DOI : 10.1016/0165-0114(95)00267-7

C. Carlsson and R. Fuller, Fuzzy reasoning in decision making and optimization, 2012.
DOI : 10.1007/978-3-7908-1805-5

S. Chanas and D. Kuchta, Linear programming problem with fuzzy coefficients in the objective function. Fuzzy Optimization, pp.148-157, 1994.

S. Chanas and D. Kuchta, Multiobjective programming in optimization of interval objective functions ??? A generalized approach, European Journal of Operational Research, vol.94, issue.3, pp.594-598, 1996.
DOI : 10.1016/0377-2217(95)00055-0

G. Chavent and J. Jaffré, Mathematical models and finite elements for reservoir simulation, 1982.

M. Christie and M. Blunt, Tenth spe comparative solution project : A comparison of upscaling techniques, In SPE Reservoir Simulation Symposium, 2001.

A. R. Conn, K. Scheinberg, V. , and L. N. , Introduction to derivative-free optimization, 2009.
DOI : 10.1137/1.9780898718768

A. R. Conn, V. , and L. N. , Bilevel derivative-free optimization and its application to robust optimization, Optimization Methods and Software, vol.27, issue.3, pp.561-577, 2012.
DOI : 10.1007/978-1-4615-6305-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.414.2327

D. Veiga, S. Marrel, and A. , Gaussian process modeling with inequality constraints, Annales de la Faculté des Sciences de Toulouse, pp.529-555, 2012.
DOI : 10.5802/afst.1344

M. Delgado, J. Verdegay, and M. Vila, Relating different approaches to solve linear programming problems with imprecise costs, Fuzzy Sets and Systems, vol.37, issue.1, pp.33-42, 1990.
DOI : 10.1016/0165-0114(90)90061-A

D. Dubois and H. Prade, Fuzzy Sets and Systems, Academic Pr, 1980.

M. Ehrgott, Multicriteria optimization, 2006.
DOI : 10.1007/978-3-662-22199-0

A. Esogbue, Computational and data acquisition issues in fuzzy dynamic programming, Proceedings of ORSA/TIMS Conference, 1991.

A. O. Esogbue and J. Kacprzyk, Fuzzy dynamic programming. In Fuzzy sets in decision analysis, operations research and statistics, pp.281-307, 1998.

K. Fang, R. Li, and A. Sudjianto, Design and modeling for com-puter experiments, 2005.

K. Fessart and J. Lonchampt, Optimisation d'un programme d'investissements : méthode IPOP. Conférence lambda-mu, 2010.

F. Floris, M. Bush, M. Cuypers, F. Roggero, and A. Syversveen, Methods for quantifying the uncertainty of production forecasts: a comparative study, Petroleum Geoscience, vol.7, issue.S, pp.87-96, 2001.
DOI : 10.1144/petgeo.7.S.S87

F. Fongang and D. , Optimization under uncertainties Master's thesis, École Nationale Supérieure des Mines de Saint-Étienne, 2011.

V. Gabrel, C. Murat, and A. Thiele, Recent advances in robust optimization and robustness : An overview, 2012.
DOI : 10.1016/j.ejor.2013.09.036

R. Garcia-brotons, Optimisation globale : application au problème de placement de puits en ingénierie de réservoir, 2012.

C. Gardet, L. Ravalec, M. Gloaguen, and E. , Multiscale Parameterization of Petrophysical Properties for Efficient History-Matching, Mathematical Geosciences, vol.22, issue.1, pp.315-336, 2014.
DOI : 10.1007/s11004-013-9480-3

S. Gratton, M. Mouffe, A. Sartenaer, P. L. Toint, T. et al., Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization, Optimization Methods and Software, vol.25, issue.3, pp.359-386, 2010.
DOI : 10.1080/10556780903239295

S. Gratton, C. Royer, L. Vicente, and Z. Zhang, Direct Search Based on Probabilistic Descent, SIAM Journal on Optimization, vol.25, issue.3, 2014.
DOI : 10.1137/140961602
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.640.8472

P. Grzegorzewski, Nearest interval approximation of a fuzzy number. Fuzzy Sets and systems, pp.321-330, 2002.

N. Hansen and A. Ostermeier, Convergence properties of evolution strategies with the derandomized covariance matrix adaptation : The (µ/µ i , ?) ? cma ? es, Eufit, vol.97, pp.650-654, 1997.

M. Hanss, Applied fuzzy arithmetic, 2005.

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1214/aoms/1177730491

W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search, Journal of Global Optimization, vol.14, issue.4, pp.331-355, 1999.
DOI : 10.1023/A:1008382309369

C. Igel, N. Hansen, R. , and S. , Covariance Matrix Adaptation for Multi-objective Optimization, Evolutionary Computation, vol.15, issue.1, pp.1-28, 2007.
DOI : 10.1109/TEVC.2003.810758
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.469.4052

M. Inuiguchi, Robust optimization by fuzzy linear programming In Managing Safety of Heterogeneous Systems, pp.219-239, 2012.

M. Inuiguchi, H. Ichihashi, and H. Tanaka, Fuzzy programming : a survey of recent developments. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, pp.45-68, 1990.

M. Inuiguchi, R. , and J. , Possibilistic linear programming : a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy sets and systems 111, pp.3-28, 2000.

M. Inuiguchi and M. Sakawa, Robust optimization under softness in a fuzzy linear programming problem, International Journal of Approximate Reasoning, vol.18, issue.1-2, pp.21-34, 1998.
DOI : 10.1016/S0888-613X(97)10002-0

H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization of the interval objective function, European Journal of Operational Research, vol.48, issue.2, pp.219-225, 1990.
DOI : 10.1016/0377-2217(90)90375-L

J. Janusevskis, L. Riche, and R. , Simultaneous kriging-based estimation and optimization of mean response, Journal of Global Optimization, vol.10, issue.4, pp.313-336, 2013.
DOI : 10.1007/s10898-011-9836-5
URL : https://hal.archives-ouvertes.fr/emse-00674460

D. R. Jones, M. Schonlau, W. , and W. J. , Efficient global optimization of expensive black-box functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of ICNN'95, International Conference on Neural Networks, p.1942, 1948.
DOI : 10.1109/ICNN.1995.488968

S. Kirkpatrick, Optimization by simulated annealing: Quantitative studies, Journal of Statistical Physics, vol.21, issue.5-6, pp.5-6, 1984.
DOI : 10.1007/BF01009452

J. P. Kleijnen, Design and analysis of simulation experiments, 2007.
DOI : 10.1007/978-3-319-18087-8

K. Lie, An introduction to reservoir simulation using matlab : User guid for the matlab reservoir simulation toolbox (mrst), SINTEF ICT, 2014.

K. Lie, S. Krogstad, I. S. Ligaarden, J. R. Natvig, H. M. Nilsen et al., Open-source MATLAB implementation of consistent discretisations on complex grids, Computational Geosciences, vol.13, issue.2, pp.297-322, 2012.
DOI : 10.1007/s10596-011-9244-4

S. Liu, Quadratic programming with fuzzy parameters: A membership function approach, Chaos, Solitons & Fractals, vol.40, issue.1, pp.237-245, 2009.
DOI : 10.1016/j.chaos.2007.07.054

S. Liu, A revisit to quadratic programming with fuzzy parameters, Chaos, Solitons & Fractals, vol.41, issue.3, pp.1401-1407, 2009.
DOI : 10.1016/j.chaos.2008.04.061

S. Liu, A fuzzy modeling for fuzzy portfolio optimization, Expert Systems with Applications, vol.38, issue.11, pp.13803-13809, 2011.
DOI : 10.1016/j.eswa.2011.04.183

W. A. Lodwick, Fuzzy Optimization : Recent Advances and Applications, 2010.

M. Luhandjula, Fuzzy stochastic linear programming: Survey and future research directions, European Journal of Operational Research, vol.174, issue.3, pp.1353-1367, 2006.
DOI : 10.1016/j.ejor.2005.07.019

M. K. Luhandjula, Fuzzy mathematical programming : Theory, applications and extension, Journal of Uncertain Systems, vol.1, issue.2, pp.124-136, 2007.

M. K. Luhandjula, Fuzzy optimization : Milestones and perspectives. Fuzzy Sets and Systems Fuzzy Modeling for Optimisation and Decision, pp.4-11, 2015.
DOI : 10.1016/j.fss.2014.01.004

M. K. Luhandjula and M. Rangoaga, An approach for solving a fuzzy multiobjective programming problem, European Journal of Operational Research, vol.232, issue.2, pp.249-255, 2014.
DOI : 10.1016/j.ejor.2013.05.040

Y. Maday, N. C. Nguyen, A. T. Patera, and S. H. Pau, A general multipurpose interpolation procedure: the magic points, Communications on Pure and Applied Analysis, vol.8, issue.1, pp.383-404, 2009.
DOI : 10.3934/cpaa.2009.8.383
URL : https://hal.archives-ouvertes.fr/hal-00174797

J. R. Martins, P. Sturdza, A. , and J. J. , The complex-step derivative approximation, ACM Transactions on Mathematical Software, vol.29, issue.3, pp.245-262, 2003.
DOI : 10.1145/838250.838251
URL : https://hal.archives-ouvertes.fr/hal-01483287

M. D. Mckay, R. J. Beckman, and W. J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

R. Moore, Interval analysis, 1966.

V. Moutoussamy, S. Nanty, and B. Pauwels, Emulators for stochastic simulation codes, ESAIM : Proceedings and Surveys 48, pp.116-155, 2015.
DOI : 10.1051/proc/201448005
URL : https://hal.archives-ouvertes.fr/hal-01011770

E. A. Nadaraya, On Estimating Regression, Theory of Probability & Its Applications, vol.9, issue.1, pp.141-142, 1964.
DOI : 10.1137/1109020

S. Nasseri, Fuzzy nonlinear optimization, The Journal of Nonlinear Sciences and its Applications, vol.1, issue.4, pp.230-235, 2008.

J. A. Nelder, M. , and R. , A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-313, 1965.
DOI : 10.1093/comjnl/7.4.308
URL : http://comjnl.oxfordjournals.org/cgi/content/short/7/4/308

S. Orlovski, Mathematical programming problems with fuzzy parameters. Management decision support systems using fuzzy sets and possibility theory, pp.136-145, 1985.

E. Parzen, On estimation of a probability density function and mode. The annals of mathematical statistics, pp.1065-1076, 1962.

M. J. Powell, Restart procedures for the conjugate gradient method, Mathematical Programming, vol.11, issue.1, pp.241-254, 1977.
DOI : 10.1007/BF01593790

J. Ramík, Optimal solutions in optimization problem with objective function depending on fuzzy parameters. Fuzzy sets and systems 158, pp.1873-1881, 2007.

J. Ramík, Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy sets and systems, pp.123-138, 1985.

J. Ramsay, Functional data analysis, 2006.

B. J. Reich, E. Kalendra, C. B. Storlie, H. D. Bondell, and M. Fuentes, Variable selection for high dimensional Bayesian density estimation: application to human exposure simulation, Journal of the Royal Statistical Society: Series C (Applied Statistics), vol.64, issue.1, pp.47-66, 2012.
DOI : 10.1111/j.1467-9876.2011.00772.x

R. Rigby and D. Stasinopoulos, Construction of Reference Centiles Using Mean and Dispersion Additive Models, Journal of the Royal Statistical Society: Series D (The Statistician), vol.49, issue.1, pp.41-50, 2000.
DOI : 10.1111/1467-9884.00218

L. M. Rios and N. Sahinidis, Derivative-free optimization: a review of algorithms and comparison of software implementations, Journal of Global Optimization, vol.18, issue.3, pp.1-47, 2012.
DOI : 10.1007/s10898-012-9951-y

H. Rommelfanger, Inequality relations in fuzzy constraints and its use in linear fuzzy optimization. The Interface between Artificial Intelligence and Operations Research in Fuzzy Environment, pp.195-211, 1989.

H. Rommelfanger, R. Hanuscheck, and J. Wolf, Linear programming with fuzzy objectives. Fuzzy sets and systems, pp.31-48, 1989.
DOI : 10.1016/0165-0114(89)90134-6

H. J. Rommelfanger, Fuzzy linear programming and applications, European Journal of Operational Research, vol.92, issue.3, pp.512-527, 1996.
DOI : 10.1016/0377-2217(95)00008-9

M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics, vol.27, issue.3, pp.832-837, 1956.
DOI : 10.1214/aoms/1177728190

A. Ruziyeva, Fuzzy Bilevel Optimization, 2013.

J. Sacks, W. J. Welch, T. J. Mitchell, W. , and H. P. , Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-423, 1989.
DOI : 10.1214/ss/1177012413
URL : http://projecteuclid.org/download/pdf_1/euclid.ss/1177012413

M. Sakawa, Fuzzy multiobjective and multilevel optimization In Multiple criteria optimization : State of the art annotated bibliographic surveys, pp.171-226, 2002.

M. Sakawa, Fuzzy sets and interactive multiobjective optimization, 2013.
DOI : 10.1007/978-1-4899-1633-4

M. Sasena, P. Papalambros, and P. Goovaerts, Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization, Engineering Optimization, vol.34, issue.3, pp.263-278, 2002.
DOI : 10.1080/03052150211751

B. O. Shubert, A Sequential Method Seeking the Global Maximum of a Function, SIAM Journal on Numerical Analysis, vol.9, issue.3, pp.379-388, 1972.
DOI : 10.1137/0709036

R. C. Silva, C. Cruz, J. L. Verdegay, and A. Yamakami, A Survey of Fuzzy Convex Programming Models, pp.127-143, 2010.
DOI : 10.1007/978-3-642-13935-2_6

A. L. Soyster, Technical Note???Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming, Operations Research, vol.21, issue.5, pp.5-1154, 1973.
DOI : 10.1287/opre.21.5.1154

H. Tanaka and K. Asai, Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and systems 13, pp.1-10, 1984.
DOI : 10.1016/0165-0114(84)90022-8

H. Tanaka, P. Guo, and I. B. Türksen, Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy sets and systems, pp.387-397, 2000.
DOI : 10.1016/s0165-0114(98)00041-4
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.5417

H. Tanaka, H. Ichihashi, and K. Asai, A value of information in flp problems via sensitivity analysis. Fuzzy Sets and Systems, pp.119-129, 1986.

H. Tanaka, T. Okuda, and K. Asai, On Fuzzy-Mathematical Programming, Journal of Cybernetics, vol.3, issue.4, pp.37-46, 1973.
DOI : 10.1080/01969727308545912

H. Tanaka, T. Okuda, and K. Asai, On decision-making in fuzzy environment Fuzzy information and decision making, International Journal of Production Research, vol.23, issue.6, pp.623-635, 1977.
DOI : 10.1016/0022-247X(68)90078-4

J. Tang, W. , and D. , An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objective and resources, Computers & Operations Research, vol.24, issue.5, pp.413-422, 1997.
DOI : 10.1016/S0305-0548(96)00059-7

J. Tang, W. , and D. , A nonsymmetric model for fuzzy nonlinear programming problems with penalty coefficients, Computers & Operations Research, vol.24, issue.8, pp.717-725, 1997.
DOI : 10.1016/S0305-0548(96)00092-5

V. Torczon, On the Convergence of Pattern Search Algorithms, SIAM Journal on Optimization, vol.7, issue.1, pp.1-25, 1997.
DOI : 10.1137/S1052623493250780

L. N. Vicente, Worst case complexity of direct search, EURO Journal on Computational Optimization, vol.133, issue.1-2, pp.143-153, 2013.
DOI : 10.1007/s13675-012-0003-7

D. Wang, An inexact approach for linear programming problems with fuzzy objective and resources. Fuzzy Sets and Systems, pp.61-68, 1997.

S. Wang and J. Watada, Fuzzy stochastic optimization : theory, models and applications, 2012.
DOI : 10.1007/978-1-4419-9560-5

G. S. Watson, Smooth regression analysis Sankhy¯ a : The Indian, Journal of Statistics, Series A, pp.359-372, 1964.

H. Wu, The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with fuzzy-valued objective functions, Fuzzy Optimization and Decision Making, vol.8, issue.1, pp.1-28, 2009.
DOI : 10.1007/s10700-009-9049-2

Z. Mezghani and I. , Analyse statistique et planification d'expérience en ingénierie de réservoir, 2000.

L. Zadeh, Pruf and its application to inference from fuzzy propositions, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications, pp.1359-1360, 1977.
DOI : 10.1109/CDC.1977.271515

L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, vol.1, issue.1, pp.3-28, 1978.
DOI : 10.1016/0165-0114(78)90029-5

L. Zadeh, A. Fuzzy sets, pp.338-353, 1965.
URL : https://hal.archives-ouvertes.fr/hal-00105883

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning???I, Information Sciences, vol.8, issue.3, pp.199-249, 1975.
DOI : 10.1016/0020-0255(75)90036-5

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning???II, Information Sciences, vol.8, issue.4, pp.301-357, 1975.
DOI : 10.1016/0020-0255(75)90046-8

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-III, Information Sciences, vol.9, issue.1, pp.43-80, 1975.
DOI : 10.1016/0020-0255(75)90017-1

H. Zimmermann, Description and optimization of fuzzy systems, International Journal of General System, vol.2, issue.1, pp.209-215, 1975.