相关论文: A non-classical class of variational problems

This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the…

We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…

A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…

We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…

This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…

Accurate triangulation of the domain plays a pivotal role in computing the numerical approximation of the differential operators. A good triangulation is the one which aids in reducing discretization errors. In a standard collocation…

This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…

Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…

In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…

A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow with overdetermined condition on the free boundary is proposed. The idea of the method is to transform the governing equations to a boundary…

We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…

Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…

Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretization prescription for classical initial value problems (IVPs).…

Extreme Value Theory (EVT) is one of the most commonly used approaches in finance for measuring the downside risk of investment portfolios, especially during financial crises. In this paper, we propose a novel approach based on EVT called…

Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[…

This paper introduces a new class of variational inequalities where the obstacle is placed in the exterior domain that is disjoint from the observation domain. This is carried out with the help of nonlocal fractional operators. The need for…

We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…

For this equation we consider a final-boundary value problem with non-classical conditions not requiring agreement conditions. Equivalence of these conditions with the classic boundary condition is substantiated in the case if the solution…

The eigenvector-dependent nonlinear eigenvalue problem (NEPv) $A(P)V=V\Lambda$, where the columns of $V\in\mathbb{C}^{n\times k}$ are orthonormal, $P=VV^{\mathrm{H}}$, $A(P)$ is Hermitian, and $\Lambda=V^{\mathrm{H}}A(P)V$, arises in many…