Results on Solution Set in Certain Interval-Valued Controlled Models
In this paper, a class of controlled variational control models is studied by considering the notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>...
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2025-01-01
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| author | Savin Treanţă Omar Mutab Alsalami |
| author_facet | Savin Treanţă Omar Mutab Alsalami |
| author_sort | Savin Treanţă |
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| description | In this paper, a class of controlled variational control models is studied by considering the notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>w</mi><mo>)</mo><mo>−</mo><mi>π</mi></mrow></semantics></math></inline-formula>-invexity. Our aim is to investigate a solution set in the considered interval-valued controlled models. To achieve this, we establish some characterization results of solutions in the controlled interval-valued variational models. More precisely, necessary and sufficient conditions of optimality are highlighted as part of a feasible solution. To prove that the optimality conditions are sufficient, we impose generalized invariant convexity hypotheses for the involved multiple integral functionals. Finally, a duality result is provided in order to better describe the problem under study. The methodology used in this paper is a combination of techniques from the Lagrange–Hamilton theory, calculus of variations, and control theory. This study could be immediately improved by including an analysis of this class of optimization problems by using curvilinear integrals instead of multiple integrals. The independence of path imposed to these functionals and their physical significance would increase the applicability and importance of the paper. |
| format | Article |
| id | doaj-art-1348c6fe3970440582d3e9d4315ee011 |
| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
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| series | Mathematics |
| spelling | doaj-art-1348c6fe3970440582d3e9d4315ee0112025-01-24T13:39:43ZengMDPI AGMathematics2227-73902025-01-0113220210.3390/math13020202Results on Solution Set in Certain Interval-Valued Controlled ModelsSavin Treanţă0Omar Mutab Alsalami1Department Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, RomaniaDepartment of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi ArabiaIn this paper, a class of controlled variational control models is studied by considering the notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>w</mi><mo>)</mo><mo>−</mo><mi>π</mi></mrow></semantics></math></inline-formula>-invexity. Our aim is to investigate a solution set in the considered interval-valued controlled models. To achieve this, we establish some characterization results of solutions in the controlled interval-valued variational models. More precisely, necessary and sufficient conditions of optimality are highlighted as part of a feasible solution. To prove that the optimality conditions are sufficient, we impose generalized invariant convexity hypotheses for the involved multiple integral functionals. Finally, a duality result is provided in order to better describe the problem under study. The methodology used in this paper is a combination of techniques from the Lagrange–Hamilton theory, calculus of variations, and control theory. This study could be immediately improved by including an analysis of this class of optimization problems by using curvilinear integrals instead of multiple integrals. The independence of path imposed to these functionals and their physical significance would increase the applicability and importance of the paper.https://www.mdpi.com/2227-7390/13/2/202controlled variational modelsoptimal pair(<i>q</i>,<i>w</i>) − <i>π</i>-invexitydual problemfeasible solution |
| spellingShingle | Savin Treanţă Omar Mutab Alsalami Results on Solution Set in Certain Interval-Valued Controlled Models Mathematics controlled variational models optimal pair (<i>q</i>,<i>w</i>) − <i>π</i>-invexity dual problem feasible solution |
| title | Results on Solution Set in Certain Interval-Valued Controlled Models |
| title_full | Results on Solution Set in Certain Interval-Valued Controlled Models |
| title_fullStr | Results on Solution Set in Certain Interval-Valued Controlled Models |
| title_full_unstemmed | Results on Solution Set in Certain Interval-Valued Controlled Models |
| title_short | Results on Solution Set in Certain Interval-Valued Controlled Models |
| title_sort | results on solution set in certain interval valued controlled models |
| topic | controlled variational models optimal pair (<i>q</i>,<i>w</i>) − <i>π</i>-invexity dual problem feasible solution |
| url | https://www.mdpi.com/2227-7390/13/2/202 |
| work_keys_str_mv | AT savintreanta resultsonsolutionsetincertainintervalvaluedcontrolledmodels AT omarmutabalsalami resultsonsolutionsetincertainintervalvaluedcontrolledmodels |