Related papers: Differentiability of the value function in control…
In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator…
In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
In this paper we study a problem of looking for an optimal solution of a system of the differential equations with a control and an optimized function. The system of differential equations is changed for two systems with the upper and lower…
We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…
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 paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…
Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
We consider notions of weak solutions to a general class of parabolic problems of linear growth, formulated independently of time regularity. Equivalence with variational solutions is established using a stability result for weak solutions.…
The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus…
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…
Differential stability of convex discrete optimal control problems in Banach spaces is studied in this paper. By using some recent results of An and Yen [Appl. Anal. 94, 108--128 (2015)] on differential stability of parametric convex…
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting…
We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…
Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…
This paper studies the differentiability of the value function of switched linear systems under arbitrary switching and controlled switching, referred to as worst-case and optimal value functions respectively. First, we show that the value…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…