Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems
One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptio...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/983643 |
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| author | W. A. Oliveira A. Beato-Moreno A. C. Moretti L. L. Salles Neto |
| author_facet | W. A. Oliveira A. Beato-Moreno A. C. Moretti L. L. Salles Neto |
| author_sort | W. A. Oliveira |
| collection | DOAJ |
| description | One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms. |
| format | Article |
| id | doaj-art-ac5a3338c43d4923a608d161465b6d1d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ac5a3338c43d4923a608d161465b6d1d2025-02-03T05:52:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/983643983643Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization ProblemsW. A. Oliveira0A. Beato-Moreno1A. C. Moretti2L. L. Salles Neto3School of Applied Sciences, State University of Campinas, 13484-350 Limeira, SP, BrazilDepartment of Statistics and Operations Research, College of Mathematics, University of Sevilla, 41012 Sevilla, SpainSchool of Applied Sciences, State University of Campinas, 13484-350 Limeira, SP, BrazilDepartment of Science and Technology, Federal University of São Paulo, 12247-014 São José dos Campos, SP, BrazilOne of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.http://dx.doi.org/10.1155/2014/983643 |
| spellingShingle | W. A. Oliveira A. Beato-Moreno A. C. Moretti L. L. Salles Neto Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems Journal of Applied Mathematics |
| title | Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems |
| title_full | Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems |
| title_fullStr | Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems |
| title_full_unstemmed | Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems |
| title_short | Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems |
| title_sort | pareto optimality conditions and duality for vector quadratic fractional optimization problems |
| url | http://dx.doi.org/10.1155/2014/983643 |
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