相关论文: Second-order conditions for spatio-temporally spar…

In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…

Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…

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 unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…

Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate…

From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…

In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…

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…

We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…

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…

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…

We consider a bilinear optimal control problem associated to the following chemotaxis-consumption model in a bounded domain $\Omega \subset \mathbb{R}^3$ during a time interval $(0,T)$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla…

The aim of this note is to give a geometric insight into the classical second order optimality conditions for equality-constrained minimization problem. We show that the Hessian's positivity of the Lagrangian function associated to the…

This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…

This paper provides a framework for deriving a new set of necessary conditions for adverse control problems among two players. The distinguish feature of such problems is that the first player has a priori knowledge on the second player…

In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic evolution equations in Hilbert…

Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…

In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…