相关论文: Computing Optimal Designs of multiresponse Experim…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
This paper proposes a second-order conic programming (SOCP) approach to solve distributionally robust two-stage stochastic linear programs over 1-Wasserstein balls. We start from the case with distribution uncertainty only in the objective…
Stochastic Optimal Control Problems (SOCPs) plays a major role in the sequential decision-making challenges. There exist various iterative algorithms, under framework of stochastic maximum principle, that sequentially find the optimal…
We consider the optimal experimental design problem of allocating subjects to treatment or control when subjects participate in multiple, separate controlled experiments within a short time-frame and subject covariate information is…
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this…
We give a new characterization of Elfving's (1952) method for computing c-optimal designs in k dimensions which gives explicit formulae for the k unknown optimal weights and k unknown signs in Elfving's characterization. This eliminates the…
The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio (SINR), incorporating a positive semidefinite constraint…
Let the design of an experiment be represented by an $s$-dimensional vector $\mathbf {w}$ of weights with nonnegative components. Let the quality of $\mathbf {w}$ for the estimation of the parameters of the statistical model be measured by…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
In this paper, we propose a new convergent conic programming hierarchy of relaxations involving both semi-definite cone and second-order cone constraints for solving nonconvex polynomial optimization problems to global optimality. The…
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…
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…
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…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The $c$-optimal design problem is investigated in the case when the parameters of both the…
$E$-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]…
In this paper, we introduce a primal-dual algorithmic framework for solving Symmetric Cone Programs (SCPs), a versatile optimization model that unifies and extends Linear, Second-Order Cone (SOCP), and Semidefinite Programming (SDP). Our…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…