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T-optimal designs for multi-factor polynomial regression models via a semidefinite relaxation method

机译：半确定松弛法的多元多项式回归模型的T最优设计

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摘要

We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets. Our proposed optimality criterion is formulated as a convex optimization problem with a moment cone constraint. When the regression models have one factor, an exact semidefinite representation of the moment cone constraint can be applied to obtain an equivalent semidefinite program. When there are two or more factors in the models, we apply a moment relaxation technique and approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When the relaxation hierarchy converges, an optimal discrimination design can be recovered from the optimal moment matrix, and its optimality can be additionally confirmed by an equivalence theorem. The methodology is illustrated with several examples.
机译：我们考虑用于区分多因素多项式回归模型的T最优实验设计问题，其中设计空间由多项式不等式定义，并且回归参数被约束到给定的凸集。我们提出的最优准则被公式化为具有矩锥约束的凸优化问题。当回归模型具有一个因子时，可以应用矩锥约束的精确半定表示来获得等效的半定程序。当模型中有两个或两个以上因素时，我们应用矩松弛技术，并通过半定性可表示的外部近似层次来近似矩锥约束。当松弛层次收敛时，可以从最优矩矩阵中恢复最优判别设计，并且可以通过等价定理进一步确认其最优性。通过几个示例说明了该方法。

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