Bui Trong Kien

On the solution existence of pseudomonotone variational inequalities

As shown by Thanh Hao [Acta Math. Vietnam 31, 283–289, 2006], the solution existence results established by Facchinei and Pang [Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I (Springer, Berlin, 2003) Prop. 2.2.3 and Theorem 2.3.4] for variational inequalities (VIs) in general and for pseudomonotone VIs in particular, are very useful for studying the range of applicability of the Tikhonov regularization method. This paper proposes some extensions of these results of Facchinei and Pang to the case of generalized variational inequalities (GVI) and of variational inequalities in infinite-dimensional reflexive Banach spaces. Various examples are given to analyze in detail the obtained results.

Subgradients of value functions in parametric dynamic programming

We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Frechet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Frechet subdifferential of value functions in parametric dynamic programming are obtained.

Degree theory for generalized variational inequalities and applications

In this paper, a degree theory for finite dimensional generalized variational inequalities is built and employed to prove some results on solution existence and solution stability.

Second-Order Necessary Optimality Conditions for a Class of Semilinear Elliptic Optimal Control Problems with Mixed Pointwise Constraints

This paper deals with first- and second-order necessary optimality conditions for a class of optimal control problems governed by semilinear elliptic partial differential equations with mixed pointwise state-control constraints.

Further Results on Subgradients of the Value Function to a Parametric Optimal Control Problem

This paper studies the first-order behavior of the value function of a parametric optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Fréchet subdifferential of the value function of a parametric minimization problem, we derive a formula for computing the Fréchet subdifferential of the value function to a parametric optimal control problem. The obtained results improve and extend some previous results.

On the solution stability of variational inequalities

AbstractIn the present paper, we will study the solution stability of parametric variational conditions

Necessary Conditions for Multiobjective Optimal Control Problems with Free End-Time

{{0 \in f(\mu, x)+ N_{K(\lambda)}(x)},}

Pontryagin's Principle for Optimal Control Problem Governed by 3D Navier---Stokes Equations

where M and Λ are topological spaces,