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Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and…
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…
In many resource-limited optimal control problems, multiple constraints may be enforced that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we…
In this paper, we consider ensembles of control-affine systems in $\mathbb{R}^d$, and we study simultaneous optimal control problems related to the worst-case minimization. After proving that such problems admit solutions, denoting with…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
In this short note, we discuss how the optimality conditions for the problem of minimizing a multivariate function subject to equality constraints have been dealt with in undergraduate Calculus. We are particularly interested in the 2 or…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossible, to check. By taking advantage of several relaxations of…