Innovative CVX-based algorithms for Optimal Design Problems on Discretized Regions

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dc.contributor.authorAbousaleh, Hanan
dc.contributor.supervisorZhou, Julie
dc.date.accessioned2023-12-05T00:30:15Z
dc.date.copyright2023en_US
dc.date.issued2023-12-04
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractWe focus on a class of optimization problems known as optimal design problems, where the goal is to select design points optimally with respect to some criterion of interest. For regression models, the optimality criterion is based on the statistical model itself and is often a function of the information matrix. We solve A-, D-, and EI-optimal design problems in this thesis. The CVX program in MATLAB is a modelling tool and solver for convex optimization problems. As with other numerical methods in the literature, formulating an optimal design problem in a CVX-compatible way requires a discrete design space. We develop a CVX-based algorithm to solve optimal design problems on large and irregular discrete spaces for multiple regression models. The algorithm uses innovative rules to add several design points at each iteration, and clusters nearby points together at the end of iteration. Furthermore, we provide useful guidelines for discretizing irregular regions. These are based on derived theoretical properties which relate optimal designs on continuous and discrete design spaces. Several numerical examples and their MATLAB codes are presented for A-, D-, and EI-optimal designs for both linear and generalized linear models. The optimal designs found via the CVX solver are better than those presented in the literature. In addition, our guidelines to discretizing design spaces improve the efficiency of optimal designs, especially over irregular regions. We find that our iterative procedure overcomes the bottlenecks of typical sequential and multiplicative algorithms.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/15670
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectapproximate designsen_US
dc.subjectdiscretizationen_US
dc.subjectA-optimalityen_US
dc.subjectD-optimalityen_US
dc.subjectEI-optimalityen_US
dc.subjectCVXen_US
dc.subjectiterative methodsen_US
dc.subjectconvex optimizationen_US
dc.subjectmultiple regressionen_US
dc.subjectsequential algorithmsen_US
dc.titleInnovative CVX-based algorithms for Optimal Design Problems on Discretized Regionsen_US
dc.typeThesisen_US

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