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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 713765, 9 pages
Sufficient Efficiency Conditions for Vector Ratio Problem on the Second-Order Jet Bundle
Faculty of Applied Sciences, University “Politehnica” of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania
Received 30 January 2012; Accepted 13 February 2012
Academic Editor: Khalida Inayat Noor
Copyright © 2012 Ariana Pitea. 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.
- A. Chinchuluun and P. M. Pardalos, “A survey of recent developments in multiobjective optimization,” Annals of Operations Research, vol. 154, pp. 29–50, 2007.
- A. Chinchuluun, P. M. Pardalos, A. Migdalas, and L. Pitsoulis, Pareto Optimality, Game Theory and Equilibria, vol. 17 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2008, Edited by Altannar Chinchuluun, Panos M. Pardalos, Athanasios Migdalas and Leonidas Pitsoulis.
- Z. A. Khan and M. A. Hanson, “On ratio invexity in mathematical programming,” Journal of Mathematical Analysis and Applications, vol. 205, no. 2, pp. 330–336, 1997.
- L. V. Reddy and R. N. Mukherjee, “Some results on mathematical programming with generalized ratio invexity,” Journal of Mathematical Analysis and Applications, vol. 240, no. 2, pp. 299–310, 1999.
- M. A. Hanson, “A duality theorem in non-linear programming with non-linear constraints,” The Australian Journal of Statistics, vol. 3, pp. 64–72, 1961.
- C. Singh and M. A. Hanson, “Multiobjective fractional programming duality theory,” Naval Research Logistics, vol. 38, no. 6, pp. 925–933, 1991.
- V. Jeyakumar and B. Mond, “On generalised convex mathematical programming,” Australian Mathematical Society Journal Series B, vol. 34, no. 1, pp. 43–53, 1992.
- Z.-A. Liang, H.-X. Huang, and P. M. Pardalos, “Efficiency conditions and duality for a class of multiobjective fractional programming problems,” Journal of Global Optimization, vol. 27, no. 4, pp. 447–471, 2003.
- A. Pitea and M. Postolache, “Minimization of vectors of curvilinear functionals on the second order jet bundle. Necessary conditions,” Optimization Letters, vol. 6, no. 3, pp. 459–470, 2011.
- A. Pitea, Integral geometry and PDE constrained optimization problems, Ph.D. thesis, University “Politehnica” of Bucharest, 2008.
- C. Udrişte and M. Postolache, Atlas of Magnetic Geometric Dynamics, vol. 3, Geometry Balkan Press, Bucharest, Romania, 2001.
- C. Udrişte, O. Dogaru, and I. Ţevy, “Null Lagrangian forms and Euler-Lagrange PDEs,” Journal of Advanced Mathematical Studies, vol. 1, no. 1-2, pp. 143–156, 2008.
- A. Pitea and M. Postolache, “Duality theorems for a new class of multitime multiobjective variational problems,” Journal of Global Optimization. In press.
- A. Pitea and C. Udrişte, “Sufficient efficiency conditions for a minimizing fractional program,” “Politehnica” University of Bucharest. Scientific Bulletin, vol. 72, no. 2, pp. 13–20, 2010.
- Ş. Mititelu, “Extensions in invexity theory,” Journal of Advanced Mathematical Studies, vol. 1, no. 1-2, pp. 63–70, 2008.
- Ş. Mititelu and M. Postolache, “Mond-Weir dualities with Lagrangians for multiobjective fractional and non-fractional variational problems,” Journal of Advanced Mathematical Studies, vol. 3, no. 1, pp. 41–58, 2010.
- Ş. Mititelu, V. Preda, and M. Postolache, “Duality of multitime vector integral programming with quasiinvexity,” Journal of Advanced Mathematical Studies, vol. 4, no. 2, pp. 59–72, 2011.
- C. Nahak and R. N. Mohapatra, “Nonsmooth -invexity in multiobjective programming problems,” Optimization Letters, vol. 6, no. 2, pp. 253–260, 2012.
- A. Pitea, “Null Lagrangian forms on 2nd order jet bundles,” Journal of Advanced Mathematical Studies, vol. 3, no. 1, pp. 73–82, 2010.
- M. Postolache, “Minimization of vectors of curvilinear functionals on second order jet bundle: dual program theory,” Abstract and Applied Analysis, vol. 2012, Article ID 535416, 12 pages, 2012.