Related papers: Second order optimality conditions in a new Lagran…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous…
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point…
In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…
In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by…
Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints…
In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super…
In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…
We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.
In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization…
This paper on the whole concerns with the duality of Mayer problem for k-th order differential inclusions, where k is an arbitrary natural number. Thus, this work for constructing the dual problems to differential inclusions of any order…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear…