Related papers: Functional determinants for the second variation
The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets…
We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
We study the optimal recovery problem for isotropic functions defined by second-order differential operators using both function and gradient values. We derive the upper bound for n-th optimal error with an explicit constant, which is…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the…
We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…
We pass to the limit in the homogenization of an optimal control problem associated with a parabolic equation with a dynamic boundary condition. New unexpected terms appear due to the critical scale.
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
This paper studies optimal control under the average-reward/cost criterion for deterministic linear systems. We derive the value function and optimal policy, and propose an approximate solution using Model Predictive Control to enable…
Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
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…
We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of…