相关论文: State-constraint static Hamilton-Jacobi equations …
We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…
This paper presents Lax formulae for solving the following optimal control problems: minimize the maximum (or the minimum) cost over a time horizon, while satisfying a state constraint. We present a viscosity theory, and by applying the…
In this short note we treat a 1+1-dimensional system of changing type. On different spatial domains the system is of hyperbolic and elliptic type, that is, formally, $\partial_t^2 u_n-\partial_x^2 u_n = \partial_t f$ and $u_n-\partial_x^2…
We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove…
The Ordered Upwind Method (OUM) is used to approximate the viscosity solution of the static Hamilton-Jacobi-Bellman (HJB) with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
A central challenge in quantum simulation is to prepare low-energy states of strongly interacting many-body systems. In this work, we study the problem of preparing a quantum state that optimizes a random all-to-all, sparse or dense, spin…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
Newman and Rovelli have used singular Hamilton-Jacobi transformations to reduce the phase space of general relativity in terms of the Ashtekar variables. Their solution of the gauge constraint cannot be inverted and indeed has no Minkowski…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
The paper studies a system of Hamilton-Jacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool…
We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
We study stable solutions to fractional semilinear equations $(-\Delta)^s u = f(u)$ in $\Omega \subset \mathbb{R}^n$, for convex nonlinearities $f$, and under the Dirichlet exterior condition $u=g$ in $\mathbb{R}^n \setminus \Omega$ with…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region \Omega, within the complex plane. More precisely, we consider three types of regions and their intersections:…
We adapt the metric approach to the study of stationary ergodic Hamilton-Jacobi equations, for which a notion of admissible random (sub)solution is defined. For any level of the Hamiltonian greater than or equal to a distinguished critical…