Vector optimization problems and approximated vector optimization problems
Keywords:efficient solution, invex function, pseudoinvex function, approximation
AbstractIn this paper, a so-called approximated vector optimization problem associated to a vector optimization problem is considered. The equivalence between the efficient solutions of the approximated vector optimization problem and efficient solutions of the original optimization problem is established.
T. Antczak, Saddle Point Criteria and Duality in Multiobjective Programming via an η-Approximation Method, Anziam J., 47, pp. 155-172, 2005, https://doi.org/10.1017/s1446181100009962
T. Antczak, A new Approach to Multiobjective Programming with a Modified Objective Function, Journal of Global Optimization, 27, pp. 485-495, 2003, https://doi.org/10.1023/a:1026080604790
C.R. Bector, S. Chandra and C. Singh, A Linearization Approach to Multiobjective Programming Duality, Journal of Mathematical Analysis and Applications, 175, pp. 268-279, 1993, https://doi.org/10.1006/jmaa.1993.1167
A. Ben-Israel and B. Mond, What is Invexity?, Journal of the Australian Mathematical Society, 28B, pp. 1-9, 1986, https://doi.org/10.1017/s0334270000005142
B.D. Craven, Invex Functions and Constrained local Minima, Bulletin of the Australian Mathematical Society, 24, pp. 357-366, 1981, https://doi.org/10.1017/s0004972700004895
J.W. Chen, Y.J. Cho, J.K. Kim and J. Li, Multiobjective Optimization Problems with Modified Objective Functions and cone Constraints and Applications, Journal of Global Optimization, https://doi.org/10.1007/s10898-010-9539-3
D.I. Duca, On the Higher-Order in Nonlinear Programming in Complex Space, Seminar on Optimization Theory Cluj-Napoca, pp. 39-50, 1985, Preprint 85-5, Univ. Babeş-Bolyai, Cluj-Napoca, 1985.
D.I. Duca, Multicriteria Optimization in Complex Space, House of the Book of Science, Cluj-Napoca, 2006.
D.I. Duca, and E. Duca, Optimization Problems and η-Approximated Optimization Problems, Studia Univ. "Babeş-Bolyai", Mathematica, 54, no. 4, pp. 49-62, 2009.
M. Hanchimi and B. Aghezzaf, Sufficiency and Duality in Differentiable Multiobjective Programming Involving Generalized type I Functions, Journal of Mathematical Analysis and Applications, 296, pp. 382-392, 2004, https://doi.org/10.1016/j.jmaa.2003.12.042
M.A. Hanson, On Sufficiency of Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, 30, pp. 545-550, 1981, https://doi.org/10.1016/0022-247x(81)90123-2
O.L. Mangasarian, Nonlinear Programming, McGraw-Hill Book Company, New York, NY, 1969.
O.L. Mangasarian, Second-and Higher-Order Duality in Nonlinear Programming, Journal of Mathematical Analysis and Applications, 51, pp. 607-620, 1975, https://doi.org/10.1016/0022-247x(75)90111-0
D.H. Martin, The Essence of Invexity, Journal of Optimization Theory and Applications, 47, pp. 65-76, 1985, https://doi.org/10.1007/bf00941316
S.K. Mishra and K.K. Lai, Second Order Symmetric Duality in Multiobjective Programming Involving Generalized Cone-Invex Functions, European Journal of Operational Research, 178, no. 1, pp. 20-26, 2007, https://doi.org/10.1016/j.ejor.2005.11.024
J. Zhang and B. Mond, Second Order B-Invexity and Duality in Mathematical Programming, Utilitas Mathematica, 50, pp. 19-31, 1996.
How to Cite
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.