On Modified Interval-Valued Variational Control Problems with First-Order PDE Constraints

Treanţă, Savin

doi:10.3390/sym12030472

Cited by 13 publications

(5 citation statements)

References 15 publications

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“…Bazargan and Mohebi [17] proposed a new constraints qualification for convex optimization and Ghosh et al [18] applied the generalized Hukuhara and Frechet differences in the area of interval optimization. However, to enrich the concept of interval optimization, Treanta [19][20][21][22] introduced several concepts on the different branches of interval optimization field viz. constrained interval-valued optimization, interval-valued variational control, and saddle-point optimality problems.…”

Section: ø Fuzzy-valued Optimization Problem Interval-valued Optimiza...mentioning

confidence: 99%

A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

et al. 2021

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In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples.

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Section: ø Fuzzy-valued Optimization Problem Interval-valued Optimiza...mentioning

confidence: 99%

A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

et al. 2021

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“…Further, Treanta established dual pair of multiobjective interval-valued variational control problems. We can extend the results on multiobjective semidefinite optimization problems to variational control problems and interval-valued optimization problems motivated by [40,41,[57][58][59][60][61] for the application point of view.…”

Section: Conclusion and Future Remarksmentioning

confidence: 99%

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

et al. 2021

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In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type constraints qualification to achieve strong S—stationary conditions from Fritz John stationary conditions. Further, we establish strong S—stationary necessary and sufficient conditions, independently from Fritz John conditions. The optimality results for multiobjective semidefinite optimization problem in this paper is related to two recent articles by Treanta in 2021. Treanta in 2021 discussed duality theorems for special class of quasiinvex multiobjective optimization problems for interval-valued components. The study in our article can also be seen and extended for the interval-valued optimization motivated by Treanta (2021). Some examples are provided to validate our established results.

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“…In this respect, we mention, for instance, the research works of Mititelu, 1 Treanţȃ, 2 Olteanu and Treanţȃ, 3 Mititelu and Treanţȃ, 4 and Jayswal et al 5,6 on the study of some optimization problems with ODE, PDE, or isoperimetric constraints. But, since the difficulty of the considered problems was increasing, several auxiliary (modified) optimization problems have been introduced to study the initial problem more easily (see, quite recently, Treanţȃ [7][8][9][10] ). Moreover, since the complexity of real-life processes and phenomena is very high and often involves uncertainty in initial data, many researchers turned their attention to real problems involving higher-order PDEs, isoperimetric restrictions, uncertain data, or a combination thereof.…”

Section: Introductionmentioning

confidence: 99%

Robust saddle‐point criterion in second‐order partial differential equation and partial differential inequation constrained control problems

Treanţă

2021

Intl J Robust & Nonlinear

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In this article, for a given class of multi-dimensional scalar variational control problems (named (P)) with mixed constraints implying second-order partial differential equations and inequations, we introduce an auxiliary (modified) class of variational control problems (named (P) (b,c) ), which is much easier to study, and provide some characterization results of (P) and (P) (b,c) by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to (P) (b,c) . For this aim, we consider scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian.

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On Modified Interval-Valued Variational Control Problems with First-Order PDE Constraints

Cited by 13 publications

References 15 publications

A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

Robust saddle‐point criterion in second‐order partial differential equation and partial differential inequation constrained control problems

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