Existence theorems of optimal control problems in Banach spaces

Stochastic Optimal Control Problems and Parabolic Equations in Banach Spaces

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearity. These problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat and wave equations with co...

Lyapunov Theorems for Banach Spaces

We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for £-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary operators.

Optimal Feedback Control of Fractional Semilinear Integro-differential Equations in The Banach Spaces

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

On an Augmented Lagrangian SQP Method for a Class of Optimal Control Problems in Banach Spaces

Existence and convergence theorems for the new system of generalized mixed variational inequalities in Banach spaces

In this article, we introduce and consider the three-step iterative algorithms for solving a new system of generalized mixed variational inequalities involving different three multi-valued operators. In this study, we use a generalized f-projection method for finding the solutions of generalized system of mixed variational inequalities in Banach spaces. Our result in this article improves and g...