Related papers: Discrete time pontryagin principles in banach spac…

In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equations with pointwise delay in the state and with control dependent noise, in the general case of…

In this paper, we introduce the concept of isotone cones in Banach spaces. Then we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity…

Reliable high-fidelity quantum state transformation has always been considered as an inseparable part of quantum information processing. In this regard, Pontryagin maximum principle has proved to play an important role to achieve the…

In this paper, we consider how to construct the optimal solutions for a general discrete time infinite horizon optimal control problem. We establish necessary and sufficient conditions for optimality in the sense of a modified optimality…

We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach space are proved. To get the well-posed initial…

We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.

The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions…

This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\'etivier and Pellaumail. Those notions are…

When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…

We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…

Unique continuation properties for a class of evolution equations defined on Banach spaces are considered from two different point of views: the first one is based on the existence of conserved quantities, which very often translates into…

This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex,…

This paper outlines a novel extension of the classical Pontryagin minimum (maximum) principle to stochastic optimal control problems. Contrary to the well-known stochastic Pontryagin minimum principle involving forward-backward stochastic…

This paper provides a functional analytic approach to differential equations on Banach space with slowly evolving parameters. We develop a Fenichel-like theory for attracting subsets of critical manifolds via a Lyapunov-Perron method. This…

This paper deals with a general form of variational problems in Banach spaces which encompasses variational inequalities as well as minimization problems. We prove a characterization of local error bounds for the distance to the…

In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone…

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…

We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…

This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…

This is the first of two closely related papers on transversality. Here we introduce the notion of tangential transversality of two closed subsets of a Banach space. It is an intermediate property between transversality and…