On a modified optimal control problem with first-order PDE constraints and the associated saddle-point optimality criterion

Necessary Optimality Conditions in Isoperimetric Constrained Optimal Control Problems

“…For other connected ideas to this subject, the reader is directed to Treanţȃ [27], where several optimization problems governed by simple, multiple, or curvilinear integral functionals (involving second-order Lagrangians) subject to ODE, PDE, or isoperimetric constraints are considered. Also, Treanţȃ [28] introduced a modified multidimensional optimal control problem and established the associated saddle-point optimality criteria.…”

Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals

“…Further, in order to introduce the main results of this paper, in accordance with Treanţȃ [20], Mititelu and Treanţȃ [14], Treanţȃ [15][16][17] anf following Treanţȃ and Mititelu [21], we formulate some auxiliary mathematical tools.…”

“…According to Mititelu and Treanţȃ [14] and Treanţȃ [20], if (x 0 , v 0 ) ∈ D is an efficient solution of the problem (FP), there exist θ = (θ r ), µ(t) and λ(t), with µ(t) = (µ s (t)), λ(t) = (λ j (t)) piecewise smooth functions, fulfilling…”

“…In this paper, motivated and inspired by the aforementioned works, under (ρ, b)-quasi-invexity assumptions, a duality model of Mond-Weir type is studied for a new multiobjective fractional variational control problem governed by path-independent integral functionals (initiated by Mititelu and Treanţȃ [14]). Taking into account the necessary efficiency conditions formulated in Mititelu and Treanţȃ [14], in accordance with Treanţȃ [15][16][17][18][19][20] and following Treanţȃ and Mititelu [21], we shall formulate and prove weak, strong and converse duality results for the considered variational control problem. Due to the physical significance (mechanical work) of the functionals used, the present work also has a huge potential regarding the applicability of the obtained results.…”

On weak sharp solutions in $(\rho , \mathbf{b}, \mathbf{d})$-variational inequalities

“…In this paper, motivated and inspired by the ongoing research in this field and by using some variational techniques developed in Ansari [2], Clarke [4] and Treanţă [12][13][14][15][16], we investigate a new class of variational-type inequalities governed by (ρ, b, d)-convex pathindependent curvilinear integral functionals (a new concept introduced in Treanţă [16]). The extended concept of a normal cone (see Treanţă [16]), firstly introduced by Marcotte and Zhu [10], plays a crucial role in our investigations.…”