Related papers: Integer Optimal Control with Fractional Perimeter …
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of…
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system with quadratic cost function, we study polynomial systems…
Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…
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…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…
The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
Data dependent regularization is known to benefit a wide variety of problems in machine learning. Often, these regularizers cannot be easily decomposed into a sum over a finite number of terms, e.g., a sum over individual example-wise…
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we…
In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
We prove optimal regularity and derive several geometric properties for solutions of a free boundary problem with fractional diffusion. Additionally, we deduce local $C^{1,\alpha}$ regularity results for the corresponding interior and…
We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…