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Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…

Nonlinear optimization-based control policies, such as those those arising in nonlinear Model Predictive Control, have seen remarkable success in recent years. These policies require solving computationally demanding nonlinear optimization…

In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…

Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…

This paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree $n-2$ and $n$. In a fundamental paper, Atkinson and Fedorov [Biometrika 62 (1975a) 57--70] proposed…

Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…

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…

Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated datasets. This issue is compounded further when…

Much of the work in the literature on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters in some models. Recent work allows errors in the models to be non-normally…

Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have…

We consider design issues for toxicology studies when we have a continuous response and the true mean response is only known to be a member of a class of nested models. This class of non-linear models was proposed by toxicologists who were…

Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…

Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…

Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…

We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…

General multi-objective optimization problems are often solved by a sequence of parametric single objective problems, so-called scalarizations. If the set of nondominated points is finite, and if an appropriate scalarization is employed,…

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…

We consider the problem of identifying the most profitable product design from a finite set of candidates under unknown consumer preference. A standard approach to this problem follows a two-step strategy: First, estimate the preference of…

We propose a general methodology of sequential locally optimal design of experiments for explicit or implicit nonlinear models, as they abound in chemical engineering and, in particular, in vapor-liquid equilibrium modeling. As a sequential…

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…