Constrained variational problems governed by second-order Lagrangians

Treanţă, Savin

doi:10.1080/00036811.2018.1538501

Cited by 35 publications

(22 citation statements)

References 13 publications

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“…Following Treanţă 12,13 and taking into account Mititelu and Treanţă, 8 we introduce the definition of Kuhn‐Tucker point associated with the variational control problem ( OCP ).…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…Proof Assuming the constraint conditions (for the existence of multipliers) hold, and in accordance to Treanţă 13 (Theorem 6.1), if

(s^{0}, c^{0}) \in 𝒟

is an optimal solution in ( OCP ), then there exist a scalar

ϱ \in ℝ

and the piecewise smooth functions

μ (t) = (μ^{ι} (t)) \in ℝ^{q}, λ (t) = (λ_{i}^{ν} (t)) \in ℝ^{n m}

satisfying the following conditions

\begin{align} ϱ \frac{\partial f_{ν}}{\partial s^{i}} (t, s^{0} false(t false), c^{0} false(t false)) + λ_{i}^{ν} false(t false) \frac{\partial V_{ν}^{i}}{\partial s^{i}} (t, s^{0} false(t false), c^{0} false(t false)) \\ + μ^{ι} false(t false) \frac{\partial W_{ι}}{\partial s^{i}} (t, s^{0} false(t false), c^{0} false(t false)) + \frac{\partial λ_{i}^{ν}}{\partial t^{ν}} false(t false) = 0, i = \end{align}

…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

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A necessary and sufficient condition of optimality for a class of multidimensional control problems

Treanţă

2020

Optim Control Appl Methods

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In this paper, we introduce a necessary and sufficient condition of optimality for a new class of multidimensional optimal control problems governed by path‐independent curvilinear integral functionals and mixed constraints involving first‐order partial differential equations (PDEs) of m‐flow type. Furthermore, as a consequence, we establish the equivalence between the class of (strongly) b‐invex functionals and the class of (strongly) b‐pseudoinvex functionals. The mathematical development in the paper is supported by illustrative examples, as well.

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“…Following Treanţă 12,13 and taking into account Mititelu and Treanţă, 8 we introduce the definition of Kuhn‐Tucker point associated with the variational control problem ( OCP ).…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…Proof Assuming the constraint conditions (for the existence of multipliers) hold, and in accordance to Treanţă 13 (Theorem 6.1), if

(s^{0}, c^{0}) \in 𝒟

is an optimal solution in ( OCP ), then there exist a scalar

ϱ \in ℝ

and the piecewise smooth functions

μ (t) = (μ^{ι} (t)) \in ℝ^{q}, λ (t) = (λ_{i}^{ν} (t)) \in ℝ^{n m}

satisfying the following conditions

\begin{align} ϱ \frac{\partial f_{ν}}{\partial s^{i}} (t, s^{0} false(t false), c^{0} false(t false)) + λ_{i}^{ν} false(t false) \frac{\partial V_{ν}^{i}}{\partial s^{i}} (t, s^{0} false(t false), c^{0} false(t false)) \\ + μ^{ι} false(t false) \frac{\partial W_{ι}}{\partial s^{i}} (t, s^{0} false(t false), c^{0} false(t false)) + \frac{\partial λ_{i}^{ν}}{\partial t^{ν}} false(t false) = 0, i = \end{align}

…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

A necessary and sufficient condition of optimality for a class of multidimensional control problems

Treanţă

2020

Optim Control Appl Methods

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“…In consequence, Q(x * ) = L * , for any x * ∈ L * . Obviously, for x * ∈ L * and x ∈ L, we obtain 13) or, applying the strong b-convexity property on L of the scalar functional F(x) and the Working hypotheses, we get…”

Section: Theorem 31 Assume the Scalar Functional H(x) Is Differentiamentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Treanţă

2020

J Inequal Appl

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals

Cipu

2019

Mathematics

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Constrained variational problems governed by second-order Lagrangians

Cited by 35 publications

References 13 publications

A necessary and sufficient condition of optimality for a class of multidimensional control problems

A necessary and sufficient condition of optimality for a class of multidimensional control problems

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

Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals

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