Related papers: A dynamic programming principle with continuous so…
In this paper we investigate possible approaches to study general time-inconsistent optimization problems without assuming the existence of optimal strategy. This leads immediately to the need to refine the concept of time-consistency as…
The 0-1 integer linear programming feasibility problem is an important NP-complete problem. This paper proposes a continuous-time dynamical system for solving that problem without getting trapped in non-solution local minima. First, the…
Pontryagin type maximum principle and Bellman's dynamic programming principle serve as two of the most important tools in solving optimal control problems. There is a huge literature on the study of relationship between them. The main…
We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…
A dynamic program, as introduced by Patnaik and Immerman (1994), maintains the result of a fixed query for an input database which is subject to tuple insertions and deletions. It can use an auxiliary database whose relations are updated…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
We provide a simple and direct proof of a strong-type unique continuation principle for the fractional $p$-Laplacian $(-\Delta_p)^s$ for a range of $s$ and $p$. The result extends to strong solutions of the fractional nonlinear…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
The aim of this paper is to obtain the existence of solutions for the following fractional p-Laplacian Dirichlet problem with mixed derivatives \begin{eqnarray*}…
In this paper we study the limit as $p\to \infty$ in the evolution problem driven by the $p-$Laplacian with dynamical boundary conditions. We prove that the natural energy functional associated with this problem converges to a limit in the…
We study regularity issues and the limiting behavior as $p\to\infty$ of nonnegative solutions for elliptic equations of $p-$Laplacian type ($2 \leq p< \infty$) with a strong absorption: $$ -\Delta_p u(x) + \lambda_0(x) u_{+}^q(x) = 0 \quad…
We study the existence of solutions to systems of ordinary differential equations that involve the p-Laplacian for potentials with several global minima. We consider the connection problem for potentials with two minima in arbitrary…
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
We study the Lane-Emden system involving the logarithmic Laplacian: $$ \begin{cases} \ \mathcal{L}_{\Delta}u(x)=v^{p}(x) ,& x\in\mathbb{R}^{n},\\ \ \mathcal{L}_{\Delta}v(x)=u^{q}(x) ,& x\in\mathbb{R}^{n}, \end{cases} $$ where $p,q>1$ and…
In this paper we study optimal control problems in Wasserstein spaces, which are suitable to describe macroscopic dynamics of multi-particle systems. The dynamics is described by a parametrized continuity equation, in which the Eulerian…
In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.
This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint…
A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the…
We develop some properties of the $p-$Neumann derivative for the fractional $p-$Laplacian in bounded domains with general $p>1$. In particular, we prove the existence of a diverging sequence of eigenvalues and we introduce the evolution…