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Abstract and Applied Analysis
Volume 2013, Article ID 812125, 11 pages
Research Article

Paratingent Derivative Applied to the Measure of the Sensitivity in Multiobjective Differential Programming

Departamento de Matemática Aplicada, Escuela Politècnica Superior, Universidad de Alicante, San Vicente del Raspeig, 03080 Alicante, Spain

Received 3 February 2013; Revised 25 March 2013; Accepted 25 March 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 F. García and M. A. Melguizo Padial. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyse the sensitivity of differential programs of the form subject to where and are maps whose respective images lie in ordered Banach spaces. Following previous works on multiobjective programming, the notion of -optimal solution is used. The behaviour of some nonsingleton sets of -optimal solutions according to changes of the parameter in the problem is analysed. The main result of the work states that the sensitivity of the program is measured by a Lagrange multiplier plus a projection of its derivative. This sensitivity is measured by means of the paratingent derivative.