Vector optimization problems and approximated vector optimization problems

Authors

  • Eugenia Duca Technical University Cluj-Napoca, Romania
  • Dorel I. Duca Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat392-1031

Keywords:

efficient solution, invex function, pseudoinvex function, approximation
Abstract views: 255

Abstract

In 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.

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References

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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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.

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Published

2010-08-01

How to Cite

Duca, E., & Duca, D. I. (2010). Vector optimization problems and approximated vector optimization problems. Rev. Anal. Numér. Théor. Approx., 39(2), 122–133. https://doi.org/10.33993/jnaat392-1031

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