Related papers: Extremum conditions for functionals involving high…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…
We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory.
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
Let us consider the autonomous obstacle problem \begin{equation*} \min_v \int_\Omega F(Dv(x)) \, dx \end{equation*} on a specific class of admissible functions, where we suppose the Lagrangian satisfies proper hypotheses of convexity and…
The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
In this paper, we introduce a new second-order directional derivative and a second-order subdifferential of Hadamard type for an arbitrary nondifferentiable function. We derive several second-order optimality conditions for a local and a…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
The study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced. Necessary optimality conditions for problems of the fuzzy fractional calculus of variations with free end-points are…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the…
The goal of this paper is to derive in the two-dimensional case necessary and sufficient minimality conditions in terms of the second variation for the functional \[ v\mapsto\int_{\Omega}\big(|\nabla v|^{2}+\chi_{\{v>0\}}Q^{2} \big)\,dx, \]…
We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality…
We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms of these curves.
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain…
Stability results for extremum seeking control in $\mathbb{R}^n$ have predominantly been restricted to local or, at best, semi-global practical stability. Extending semi-global stability results of extremum-seeking systems to unbounded sets…
We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems. More general fractional action-like optimal control problems are also considered.