Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators
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 <inlin...
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2021-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/1/3 |
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| author | Kin Keung Lai Mohd Hassan Sanjeev Kumar Singh Jitendra Kumar Maurya Shashi Kant Mishra |
| author_facet | Kin Keung Lai Mohd Hassan Sanjeev Kumar Singh Jitendra Kumar Maurya Shashi Kant Mishra |
| author_sort | Kin Keung Lai |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>—</mo></mrow></semantics></math></inline-formula>stationary conditions from Fritz John stationary conditions. Further, we establish strong <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>—</mo></mrow></semantics></math></inline-formula>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. |
| first_indexed | 2024-03-10T01:28:09Z |
| format | Article |
| id | doaj.art-db90bb78beb349d991bd83431c952309 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T01:28:09Z |
| publishDate | 2021-12-01 |
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| series | Fractal and Fractional |
| spelling | doaj.art-db90bb78beb349d991bd83431c9523092023-11-23T13:48:28ZengMDPI AGFractal and Fractional2504-31102021-12-0161310.3390/fractalfract6010003Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using ConvexificatorsKin Keung Lai0Mohd Hassan1Sanjeev Kumar Singh2Jitendra Kumar Maurya3Shashi Kant Mishra4International Business School, Shaanxi Normal University, Xi’an 710119, ChinaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaKashi Naresh Government Postgraduate College, Gyanpur, Bhadohi 221304, IndiaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>—</mo></mrow></semantics></math></inline-formula>stationary conditions from Fritz John stationary conditions. Further, we establish strong <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>—</mo></mrow></semantics></math></inline-formula>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.https://www.mdpi.com/2504-3110/6/1/3multiobjective programs with vanishing constraintssemidefinite programmingconvexificatorsnonsmooth analysisconstraint qualifications |
| spellingShingle | Kin Keung Lai Mohd Hassan Sanjeev Kumar Singh Jitendra Kumar Maurya Shashi Kant Mishra Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators Fractal and Fractional multiobjective programs with vanishing constraints semidefinite programming convexificators nonsmooth analysis constraint qualifications |
| title | Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators |
| title_full | Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators |
| title_fullStr | Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators |
| title_full_unstemmed | Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators |
| title_short | Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators |
| title_sort | semidefinite multiobjective mathematical programming problems with vanishing constraints using convexificators |
| topic | multiobjective programs with vanishing constraints semidefinite programming convexificators nonsmooth analysis constraint qualifications |
| url | https://www.mdpi.com/2504-3110/6/1/3 |
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