Related papers: First and second order optimality conditions for o…
We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee…
We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…
In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
In this paper we derive necessary optimality conditions for optimal control problems with nonlinear and nonsmooth implicit control systems. Implicit control systems have wide applications including differential algebraic equations (DAEs).…
We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
In this work, we present an efficient gradient projection method for solving a class of stochastic optimal control problem with expected integral state constraint. The first order optimality condition system consisting of forward-backward…
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…
This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints (SDCMPCC).To achieve this goal, we first provide an exact characterization on the second-order…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
We consider a velocity tracking problem for stochastic Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through an injection-suction device with uncertainty, which acts in accordance with the non-homogeneous…
This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
This paper is concerned with the analysis and numerical analysis for the optimal control of first-order magneto-static equations. Necessary and sufficient optimality conditions are established through a rigorous Hilbert space approach.…
In this paper, we study two kinds of singular optimal controls (SOCs for short) problems where the systems governed by forward-backward stochastic differential equations (FBSDEs for short), in which the control has two components: the…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…