arXiv subjects

Nguyen Thanh Qui

Publications and source records attributed to Nguyen Thanh Qui.

4 recordsLinked to original sources

arXiv2020

Full Stability for Variational Nash Equilibriums of Parametric Optimal Control Problems of PDEs

This paper investigates full stability properties for \emph{variational Nash equilibriums} of a system of parametric nonconvex optimal control problems governed by semilinear elliptic partial differential equations. We first obtain some new results on the existence of variational Nash equilibriums for the system of original/parametric nonconvex optimal control problems. Then we establish explicit characterizations of the Lipschitzian and Hölderian full stability of variational Nash equilibriums under perturbations. These results deduce the equivalence between variational Nash equilibriums and local Nash equilibriums in the classical sense.

math.OC↗

arXiv2018

Subgradients of Marginal Functions in Parametric Control Problems of Partial Differential Equations

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 subgradients of the marginal function. With some additional assumptions, we show that the solution map of the perturbed optimal control problems has local upper Hölderian selections. This leads to a lower estimate for the regular subdifferential of the marginal function.

math.OC↗

arXiv2017

Full Stability for a Class of Control Problems of Semilinear Elliptic Partial Differential Equations

We investigate full Lipschitzian and full Hölderian stability for a class of control problems governed by semilinear elliptic partial differential equations, where all the cost functional, the state equation, and the admissible control set of the control problems undergo perturbations. We establish explicit characterizations of both Lipschitzian and Hölderian full stability for the class of control problems. We show that for this class of control problems the two full stability properties are equivalent. In particular, the two properties are always equivalent in general when the admissible control set is an arbitrary fixed nonempty, closed, and convex set.

math.OC↗

arXiv2017

Stability for Bang-Bang Control Problems of Partial Differential Equations

In this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first establish a sufficient optimality condition for the optimal control problems with bang-bang controls. Then we obtain criteria for solution stability for the optimal control problems of bang-bang controls under linear perturbations. We prove Hölder stability of optimal controls in $L^1$.

math.OC↗