Computing efficient exact designs of experiments using integer quadratic programming

Harman, Radoslav; Filová, Lenka

doi:10.1016/j.csda.2013.02.021

Cited by 21 publications

(28 citation statements)

References 34 publications

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“…We also remark that, using a standard computer, AQuA based on the IQP solver (unlike the specific MICQP formulation of AQuA) cannot be applied to design spaces of size larger than a few thousands, because of the quadratic memory requirements. That is, here we again demonstrated the advantage of the proposed conic AQuA approach over the approach of AQuA from Harman and Filová [13], not only over methods directly based on a MISOCP formulation of the problem as in Sagnol and Harman [34].…”

Section: D-and I-optimal Subsampling Of a Dataset Under An Upper Conssupporting

confidence: 59%

“…Harman and Filová [13] proposed a substantially different approach to the use of an optimal AD for ED construction, which overcomes many disadvantages of ER and similar methods. In particular, it does not depend on the choice of the optimal AD if the AD is not unique, it is not restricted to the support of the optimal AD, and the resulting EDs are usually significantly more efficient than the EDs computed by ER.…”

Section: Let ξ Ementioning

confidence: 99%

“…), 13 The symbols vech and vec denote the vectorization and halfvectorization of a matrix, respectively.Q…”

Section: To This End Let the Function φmentioning

confidence: 99%

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Ascent with quadratic assistance for the construction of exact experimental designs

Filová

Harman

2020

Comput Stat

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large datasets under a lower bound on the quality and an upper bound on the cost of the subsample.1 Note that we implicitly assume that reordering of the trials does not influence the relevant properties of the experimental design.2 In some experimental situations, the set of available design points can be modeled as a continuous domain. However, in many applications, the design space is finite. This is the case if each factor has -in principle or effectively -only a finite number of levels that the experimenter can select, or if the optimal design problem corresponds to data sub-selection (see the examples in Section 6). Moreover, the method proposed in this paper can also be useful for solving the problems with continuous design spaces; cf. Section 5.3 The symbols R, R + , N, N 0 , and R k×n denote the sets of real, non-negative real, natural, non-negative integer numbers, and the set of all k × n real matrices, respectively. 4 Therefore, we do not represent designs by normalized (probability) measures, as is frequently done in optimal design, but by non-normalized vectors of numbers of trials.12 Note that the matrix Q + p is symmetric, as is the matrix Q − p defined below, because tr(M 1 H 1 M 2 H 2 ) = tr(M 1 H 2 M 2 H 1 ) for the symmetric non-negative definite matrices M 1 , M 2 , H 1 , and H 2 .

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Section: D-and I-optimal Subsampling Of a Dataset Under An Upper Conssupporting

confidence: 59%

Section: Let ξ Ementioning

confidence: 99%

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Ascent with quadratic assistance for the construction of exact experimental designs

Filová

Harman

2020

Comput Stat

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“…However, the performance of these methods is not always good; the search for optimal designs is often restricted to low-dimensional models. New developments help to overcome these limitations (see Yu 2011;Sagnol 2011;Harman and Filová 2014).…”

Section: Computing Optimal Designsmentioning

confidence: 98%

Exact optimal experimental designs with constraints

2016

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The experimental design literature has produced a wide range of algorithms optimizing estimator variance for linear models where the design-space is finite or a convex polytope. But these methods have problems handling nonlinear constraints or constraints over multiple treatments. This paper presents Newton-type algorithms to compute exact optimal designs in models with continuous and/or discrete regressors, where the set of feasible treatments is defined by nonlinear constraints. We carry out numerical comparisons with other state-of-art methods to show the performance of this approach.

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“…The algorithm proposed here is in the general class of the multiplicative algorithms (Silvery, et al, 1978), which shares the simplicity and monotonic convergence property of class of the multiplicative algorithm. One of the most attractive properties of the proposed algorithm is that the convergence rate of the algorithm does not depend on the number of design points N compared to some existing algorithms such as the coordinate-exchange algorithm (Meyer and Nachtsheim, 1995) and the randomized exchange algorithm (Harman and Filová, 2014).…”

Section: Algorithm For D-optimal Designsmentioning

confidence: 99%

Efficient computational algorithm for optimal continuous experimental designs

Duan

Gao

2019

Journal of Computational and Applied Mathematics

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A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for D-optimal criterion on continuous design spaces are provided. We further show that the proposed algorithm converges to the D-optimal design. We also provide an algorithm for the A-optimality and conjecture that the algorithm convergence monotonically on continuous design spaces. Different numerical examples are used to demonstrated the usefulness and performance of the proposed algorithms.

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Computing efficient exact designs of experiments using integer quadratic programming

Cited by 21 publications

References 34 publications

Ascent with quadratic assistance for the construction of exact experimental designs

Ascent with quadratic assistance for the construction of exact experimental designs

Exact optimal experimental designs with constraints

Efficient computational algorithm for optimal continuous experimental designs

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