Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators
This article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also...
| Published in: | Axioms |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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MDPI AG
2024-07-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/8/516 |
| _version_ | 1849988584661057536 |
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| author | Ram Narayan Mohapatra Prachi Sachan Vivek Laha |
| author_facet | Ram Narayan Mohapatra Prachi Sachan Vivek Laha |
| author_sort | Ram Narayan Mohapatra |
| collection | DOAJ |
| container_title | Axioms |
| description | This article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also derive sufficient conditions for global optimality for the MPVC under convexity utilizing directional convexificators. Further, we introduce a Wolfe-type dual model in terms of directional convexificators and derive duality results. The results are well illustrated by examples. |
| format | Article |
| id | doaj-art-73c5b6ecddbc4e4e8ccacf412061fa67 |
| institution | Directory of Open Access Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-73c5b6ecddbc4e4e8ccacf412061fa672025-08-20T00:54:41ZengMDPI AGAxioms2075-16802024-07-0113851610.3390/axioms13080516Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional ConvexificatorsRam Narayan Mohapatra0Prachi Sachan1Vivek Laha2Department of Mathematics, University of Central Florida, Orlando, FL 10587, USADepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaThis article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also derive sufficient conditions for global optimality for the MPVC under convexity utilizing directional convexificators. Further, we introduce a Wolfe-type dual model in terms of directional convexificators and derive duality results. The results are well illustrated by examples.https://www.mdpi.com/2075-1680/13/8/516mathematical programs with vanishing constraintsdirectional convexificatorsoptimality conditionsconstraint qualificationsgeneralized convexity |
| spellingShingle | Ram Narayan Mohapatra Prachi Sachan Vivek Laha Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators mathematical programs with vanishing constraints directional convexificators optimality conditions constraint qualifications generalized convexity |
| title | Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators |
| title_full | Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators |
| title_fullStr | Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators |
| title_full_unstemmed | Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators |
| title_short | Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators |
| title_sort | optimality conditions for mathematical programs with vanishing constraints using directional convexificators |
| topic | mathematical programs with vanishing constraints directional convexificators optimality conditions constraint qualifications generalized convexity |
| url | https://www.mdpi.com/2075-1680/13/8/516 |
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