Journal of Applied Mathematics

Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

W. A. Oliveira, A. Beato-Moreno, A. C. Moretti, and L. L. Salles Neto

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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.

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J. Appl. Math., Volume 2014 (2014), Article ID 983643, 13 pages.

First available in Project Euclid: 2 March 2015

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Oliveira, W. A.; Beato-Moreno, A.; Moretti, A. C.; Salles Neto, L. L. Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems. J. Appl. Math. 2014 (2014), Article ID 983643, 13 pages. doi:10.1155/2014/983643.

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