A necessary and sufficient condition for duality in multiobjective variational problems

• Published in: European journal of operational research Vol. 201; no. 3; pp. 672 - 681
• Main Authors: Arana-Jiménez, M., Ruiz-Garzón, G., Rufián-Lizana, A., Osuna-Gómez, R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.03.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Decision theory. Utility theory; Efficiency; Exact sciences and technology; Mathematical functions; Multiobjective variational problem; Multiple objective programming; Multiple objective programming Nonlinear programming Multiobjective variational problem Pseudoinvexity Optimality condition; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Optimality condition; Optimization techniques; Pseudoinvexity; Studies; Optimality condition; Nonlinear programming; Multiple objective programming; Pseudoinvexity; Multiobjective variational problem; Necessary and sufficient condition; Multiobjective programming; Non linear programming; Invexity; Efficiency; Variational calculus; Optimality criterion; Kuhn Tucker method
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2009.03.047

In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to establish duality results, but it is also necessary. Moreover, these functions are characterized in order that all Kuhn–Tucker or Fritz John points are efficient solutions. Recent papers are improved. We provide an example to show this improvement and illustrate these classes of functions and results.