Related papers: Directional subdifferential of the value function

In this paper we focus on regional deterministic optimal control problems, i.e., problems where the dynamics and the cost functional may be different in several regions of the state space and present discontinuities at their interface.…

We study the budget map and the indirect utility function of a parametric consumer problem in a Banach space setting by some advanced tools from set-valued and variational analysis. The Lipschitz-likeness and differentiability properties of…

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 the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.

Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the…

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…

Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…

This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic…

Using the Fitzpatrick function, we characterize the solutions for different classes of deterministic and stochastic differential equations driven by maximal monotone operators (or in particular subdifferential operators) as the minimum…

This paper studies properties of a subdifferential defined using a generalized conjugation scheme. We relate this subdifferential together with the domain of an appropriate conjugate function and the {\epsilon}-directional derivative. In…

This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…

We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): \[ \left\{\begin{array} [c]{r} dX(t)+\partial\varphi\left(X(t)\right)…

We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space.…

Many problems involve the use of models which learn probability distributions or incorporate randomness in some way. In such problems, because computing the true expected gradient may be intractable, a gradient estimator is used to update…

In this paper, we describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in $\R^N$. This structure allows us to define a useful notion of positivity of the shape derivative and we show it…

We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where $\F$ is the class of the integrable, Lipschitz functions on…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…

This article provides a definition of a subdifferential for continuous functions based on homological considerations. We show that it satisfies all the requirement for a good notion of subdifferential. Moreover, we prove sublinearity, a…