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We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…

Optimization and Control · Mathematics 2026-04-01 Peter Gangl , Michael H. Gfrerer

We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…

Statistics Theory · Mathematics 2017-10-27 Yohann De Castro , Fabrice Gamboa , Didier Henrion , Roxana Hess , Jean-Bernard Lasserre

We present general results on D-optimal designs for estimating the mean response in repeated measures growth curve models with metric outcomes. For this situation, we derive a novel equivalence theorem for checking design optimality. The…

Statistics Theory · Mathematics 2023-01-23 Fritjof Freise , Heinz Holling , Rainer Schwabe

We provide a systematic treatment of $D$-optimal design for binary regression and quantal response models in toxicology studies. For the two-parameter case, we provide an analytical equation (WC equation) for computing the $D$-optimal…

Applications · Statistics 2022-09-28 Elvis Han Cui

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.…

Computation · Statistics 2020-02-04 Yuguang Yue , Lieven Vandenberghe , Weng Kee Wong

We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…

Statistics Theory · Mathematics 2017-05-30 Zelda Mariet , Suvrit Sra

We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange…

Computation · Statistics 2018-01-18 Radoslav Harman , Lenka Filová , Peter Richtárik

We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this…

Statistics Theory · Mathematics 2015-03-19 Jie Yang , Abhyuday Mandal , Dibyen Majumdar

Under a generalised estimating equation analysis approach, approximate design theory is used to determine Bayesian D-optimal designs. For two examples, considering simple exchangeable and exponential decay correlation structures, we compare…

Methodology · Statistics 2024-02-16 Laura Etfer , James M. S. Wason , Michael J. Grayling

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey,…

Computation · Statistics 2011-08-15 Yaming Yu

The Hadamard maximal determinant (maxdet) problem is to find the maximum determinant D(n) of a square {+1, -1} matrix of given order n. Such a matrix with maximum determinant is called a saturated D-optimal design. We consider some cases…

Combinatorics · Mathematics 2014-07-30 Richard P. Brent

In an order-of-addition experiment, each treatment is a permutation of m components. It is often unaffordable to test all the m! treatments, and the design problem arises. We consider a model that incorporates the order of each pair of…

Statistics Theory · Mathematics 2018-05-15 Jiayu Peng , Rahul Mukerjee , Dennis K. J. Lin

In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we…

Methodology · Statistics 2019-10-03 Lucy L. Gao , Julie Zhou

An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…

Data Structures and Algorithms · Computer Science 2024-03-04 Moritz Buchem , Paul Deuker , Andreas Wiese

We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…

Optimization and Control · Mathematics 2019-06-06 Victor Magron , Pierre-Loic Garoche , Didier Henrion , Xavier Thirioux

Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…

Optimization and Control · Mathematics 2009-05-18 Jean B. Lasserre

$E$-optimal experimental designs for a second-order response surface model with $k\geq1$ predictors are investigated. If the design space is the $k$-dimensional unit cube, Galil and Kiefer [J. Statist. Plann. Inference 1 (1977a) 121-132]…

Methodology · Statistics 2014-09-01 Holger Dette , Yuri Grigoriev

We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…

Optimization and Control · Mathematics 2024-01-02 Valerian-Alin Fodor , Nicolae Popovici

We study the problem of representing a discrete tensor that comes from finite uniform samplings of a multi-dimensional and multiband analog signal. Particularly, we consider two typical cases in which the shape of the subbands is cubic or…

Signal Processing · Electrical Eng. & Systems 2024-05-21 Yuhan Li , Tianyao Huang , Yimin Liu , Xiqin Wang

We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these…

Computation · Statistics 2015-04-24 Katarina Burclova , Andrej Pazman