On Controlled Variational Inequalities Involving Convex Functionals

Results on the Existence of Solutions Associated with Some Weak Vector Variational Inequalities

“…In this paper, by using the notions of the invex set, Fréchet differentiability, invexity and pseudoinvexity for the involved curvilinear integral functionals, we established some relations between the solutions of a class of weak vector variational inequalities and (weak) efficient solutions of the associated control problem. The results derived in this paper, taking into account the notion of variational derivative for curvilinear-type integral functionals (see Treanţȃ [13]), can be rediscovered in a new form.…”

“…In this regard, the reader is directed to the research work by Ruiz-Garzón et al [12]. Treanţȃ [13] studied a class of variational inequalities involving curvilinear integrals. Kim [14] established some connections between multiple-objective continuous-time problems and vector variational-type inequalities.…”

On Sufficiency Conditions for Some Robust Variational Control Problems

“…Next, in order to prove the principal results of this paper, we present the definition of convex, quasi-convex, strictly quasi-convex, and monotonic quasi-convex curvilinear integral functionals (see, for instance, Treanţȃ [21]).…”

Necessary Optimality Conditions in Isoperimetric Constrained Optimal Control Problems

“…The goal is to find an admissible control that generates a satisfactory state and extremizes the value of the objective functional (the admissible control having this property is called optimal control in the considered optimization problem). For other ideas that are connected to this subject, the reader is directed to Evans [19], Kalaba and Spingarn [20,21], Lee and Markus [22], Barbu et al [23], van Brunt [24], and Treanţȃ [25,26].…”