@misc{DuarteSagnolWong2017, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Wong, Weng Kee}, title = {An algorithm based on Semidefinite Programming for finding minimax optimal designs}, issn = {1438-0064}, doi = {10.1016/j.csda.2017.09.008}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66249}, year = {2017}, abstract = {An algorithm based on a delayed constraint generation method for solving semi-infinite programs for constructing minimax optimal designs for nonlinear models is proposed. The outer optimization level of the minimax optimization problem is solved using a semidefinite programming based approach that requires the design space be discretized. A nonlinear programming solver is then used to solve the inner program to determine the combination of the parameters that yields the worst-case value of the design criterion. The proposed algorithm is applied to find minimax optimal designs for the logistic model, the flexible 4-parameter Hill homoscedastic model and the general nth order consecutive reaction model, and shows that it (i) produces designs that compare well with minimax \$D-\$optimal designs obtained from semi-infinite programming method in the literature; (ii) can be applied to semidefinite representable optimality criteria, that include the common A-, E-,G-, I- and D-optimality criteria; (iii) can tackle design problems with arbitrary linear constraints on the weights; and (iv) is fast and relatively easy to use.}, language = {en} } @misc{DuarteSagnol2017, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume}, title = {Approximate and exact D-optimal designs for \$2^k\$ factorial experiments for Generalized Linear Models via SOCP}, issn = {1438-0064}, doi = {10.1007/s00362-018-01075-7}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66256}, year = {2017}, abstract = {We propose (Mixed Integer) Second Order Cone Programming formulations to find approximate and exact \$D-\$optimal designs for \$2^k\$ factorial experiments for Generalized Linear Models (GLMs). Locally optimal designs are addressed with Second Order Cone Programming (SOCP) and Mixed Integer Second Order Cone Programming (MISOCP) formulations. The formulations are extended for scenarios of parametric uncertainty employing the Bayesian framework for \emph{log det} \$D-\$optimality criterion. A quasi Monte-Carlo sampling procedure based on the Hammersley sequence is used for integrating the optimality criterion in the parametric region. The problems are solved in \texttt{GAMS} environment using \texttt{CPLEX} solver. We demonstrate the application of the algorithm with the logistic, probit and complementary log-log models and consider full and fractional factorial designs.}, language = {en} } @inproceedings{DuarteSagnolOliveira2015, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Oliveira, Nuno M.C.}, title = {A Robust Minimax Semidefinite Programming Formulation for Optimal Design of Experiments for Model Parametrization}, volume = {37}, booktitle = {12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering}, doi = {10.1016/B978-0-444-63578-5.50146-8}, pages = {905 -- 910}, year = {2015}, abstract = {Model-based optimal design of experiments (M-bODE) is a crucial step in model parametrization since it encloses a framework that maximizes the amount of information extracted from a battery of lab experiments. We address the design of M-bODE for dynamic models considering a continuous representation of the design. We use Semidefinite Programming (SDP) to derive robust minmax formulations for nonlinear models, and extend the formulations to other criteria. The approaches are demonstrated for a CSTR where a two-step reaction occurs.}, language = {en} } @article{DuarteSagnolWong2018, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Wong, Weng Kee}, title = {An algorithm based on Semidefinite Programming for finding minimax optimal designs}, volume = {119}, journal = {Computational Statistics \& Data Analysis}, doi = {10.1016/j.csda.2017.09.008}, pages = {99 -- 117}, year = {2018}, language = {en} } @misc{DuarteSagnolOliveira2015, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Oliveira, Nuno M.C.}, title = {A robust minimax Semidefinite Programming formulation for optimal design of experiments for model parametrization}, issn = {1438-0064}, doi = {10.1016/B978-0-444-63578-5.50146-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54626}, year = {2015}, abstract = {Model-based optimal design of experiments (M-bODE) is a crucial step in model parametrization since it encloses a framework that maximizes the amount of information extracted from a battery of lab experiments. We address the design of M-bODE for dynamic models considering a continuous representation of the design. We use Semidefinite Programming (SDP) to derive robust minmax formulations for nonlinear models, and extend the formulations to other criteria. The approaches are demonstrated for a CSTR where a two-step reaction occurs.}, language = {en} }