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The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…

Computation · Statistics 2024-06-18 Radoslav Harman , Samuel Rosa

In this paper, we derive optimal designs for the Rasch Poisson counts model and the Rasch Poisson-Gamma counts model incorporating several binary predictors for the difficulty parameter. To efficiently estimate the regression coefficients…

Methodology · Statistics 2021-04-07 Ulrike Graßhoff , Heinz Holling , Rainer Schwabe

In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory…

Optimization and Control · Mathematics 2019-12-24 Y. Xu , J. Desai , X. Yan

In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric…

Methodology · Statistics 2014-01-07 Roberto Fontana , Fabio Rapallo , Maria Piera Rogantin

We present a finite-horizon optimization algorithm that extends the established concept of Dual Dynamic Programming (DDP) in two ways. First, in contrast to the linear costs, dynamics, and constraints of standard DDP, we consider problems…

Optimization and Control · Mathematics 2018-07-17 Marc Hohmann , Joseph Warrington , John Lygeros

We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…

Optimization and Control · Mathematics 2023-09-11 Gabriel Ponte , Marcia Fampa , Jon Lee

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…

Computation · Statistics 2018-04-10 Jiangtao Duan , Wei Gao , Hon Keung Tony Ng

Semidefinite relaxations are a powerful tool for approximately solving combinatorial optimization problems such as MAX-CUT and the Grothendieck problem. By exploiting a bounded rank property of extreme points in the semidefinite cone, we…

Data Structures and Algorithms · Computer Science 2014-08-12 Roy Frostig , Sida I. Wang

Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is substantial freedom to choose where to sample. In this…

Machine Learning · Statistics 2025-08-11 Ben Adcock

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

Optimization and Control · Mathematics 2017-02-24 Andrew Lamperski , Khem Raj Ghusinga , Abhyudai Singh

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation…

Classical Analysis and ODEs · Mathematics 2009-09-18 Dmitry Batenkov

Data reduction is a fundamental challenge of modern technology, where classical statistical methods are not applicable because of computational limitations. We consider multiple linear regression for an extraordinarily large number of…

Methodology · Statistics 2025-05-30 Torsten Glemser , Rainer Schwabe

Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian $D$-optimality for non-linear regression models with covariates subject to measurement errors.…

Methodology · Statistics 2016-05-16 Maria Konstantinou , Holger Dette

Optimal design theory for nonlinear regression studies local optimality on a given design space. We identify designs for the Bradley--Terry paired comparison model with small undirected graphs and prove that every saturated D-optimal design…

Statistics Theory · Mathematics 2021-06-17 Thomas Kahle , Frank Röttger , Rainer Schwabe

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

Optimization and Control · Mathematics 2021-10-05 Xiangyi Fan , Grani A. Hanasusanto

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

Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…

Methodology · Statistics 2023-04-24 Lulu Kang , Xinwei Deng , Ran Jin

This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…

Optimization and Control · Mathematics 2024-06-18 Taotao He , Siyue Liu , Mohit Tawarmalani

Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…

Machine Learning · Computer Science 2014-02-24 Lijun Zhang , Mehrdad Mahdavi , Rong Jin , Tianbao Yang , Shenghuo Zhu

We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere $\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show that for any $f \in…

Numerical Analysis · Mathematics 2022-03-01 Amir Zandieh , Insu Han , Haim Avron