相关论文: Coisotropic Variational Problems

In the present work, we obtain the constants of motion for isoperimetric variational problems with time delay. We consider a constrained optimization problem where the Lagrangian function defining the functional depends on time delayed…

The Dirac constraint formalism is applied to linearized gravity to determine the structure of constraints and construct the canonical Hamiltonian. The diffeomorphism invariance of the Lagrangian is retrieved by a nontrivial generalization…

We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…

Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…

We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls…

In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin's maximum principle from optimal control theory for the Loewner equation in several complex…

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…

We study variational problems for curves approximated by B-spline curves. We show that, one can obtain discrete Euler-Lagrange equations, for the data describing the approximated curves. Our main application is to the curve completion…

Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently…

This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…

We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…

In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H\"{o}lder's inequalities…

We provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respective Pontryagin Hamiltonian.

In this thesis we deal with two different classes of variational problems: 1) the problem of closed curves with prescribed curvature, or $H$-loop problem; 2) the study of the nodal solutions of the fractional Brezis-Nirenberg problem. In…

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

Within the geometrical framework developed in arXiv:0705.2362, the problem of minimality for constrained calculus of variations is analysed among the class of differentiable curves. A fully covariant representation of the second variation…

This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…

We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…

Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…