Related papers: Iterative hard-thresholding applied to optimal con…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
The transformed $l_1$ penalty (TL1) functions are a one parameter family of bilinear transformations composed with the absolute value function. When acting on vectors, the TL1 penalty interpolates $l_0$ and $l_1$ similar to $l_p$ norm ($p…
Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is…
Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
This contribution considers optimal control problems subject to nonlocal conservation laws -- those in which the velocity depends nonlocally (i.e., via a convolution) on the solution -- and the so-called singular limit. First, the existence…
Compressed Sensing algorithms often make use of the hard thresholding operator to pass from dense vectors to their best s-sparse approximations. However, the output of the hard thresholding operator does not depend on any information from a…
In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…
In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to…
Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…
We study the minimization of the cost functional \[ F(\mu) = \lVert u - u_d \rVert_{L^p(\Omega)} + \alpha \lVert \mu \rVert_{\mathcal{M}(\Omega)}, \] where the controls $\mu$ are taken in the space of finite Borel measures and $u \in…
In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…
We extend the classical concepts of sampling and Euler solutions for control systems associated to discontinuous feedbacks by considering also the corresponding costs. In particular, we introduce the notions of Sample and Euler…
The naive application of Reinforcement Learning algorithms to continuous control problems -- such as locomotion and manipulation -- often results in policies which rely on high-amplitude, high-frequency control signals, known colloquially…
In this paper, we consider optimization problems with $L^0$-cost of the controls. Here, we take the support of the control as independent optimization variable. Topological derivatives of the corresponding value function with respect to…
Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds…