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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…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…
The design of complex engineering systems leads to solving very large optimization problems involving different disciplines. Strategies allowing disciplines to optimize in parallel by providing sub-objectives and splitting the problem into…
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…
In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, which considers symmetric design spaces we investigate the…
We consider the problem of obtaining information about an inaccessible half-space from acoustic measurements made in the accessible half-space. If the measurements are of limited precision, some scatterers will be undetectable because their…
We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first…
The problem of the optimal allocation (in the expected mean square error sense) of a measurement budget for particle filtering is addressed. We propose three different optimal intermittent filters, whose optimality criteria depend on the…
We present an optimal strategy having finite outcomes for estimating a single parameter of the displacement operator on an arbitrary finite dimensional system using a finite number of identical samples. Assuming the uniform {\it a priori}…
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
We clarify the mathematical structure underlying unitary $t$-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any $t$-th order polynomial over the design equals the average over the entire…
We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…
This paper considers the optimal adaptive allocation of measurement effort for identifying the best among a finite set of options or designs. An experimenter sequentially chooses designs to measure and observes noisy signals of their…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates…