Approximations of objective function and constraints in bi-criteria optimization problems

Authors

  • Traian Ionut Luca Babes-Bolyai University, Romania
  • Dorel I. Duca Babes-Bolyai University, Romania

DOI:

https://doi.org/10.33993/jnaat472-1153

Keywords:

efficient solution, bi-criteria optimization, eta-approximation, invex function, incave function, optimization
Abstract views: 248

Abstract

In this paper we study approximation methods for solving bi-criteria optimization problems.

Initial problem is approximated by a new one which has the components of the objective and the constraints are replaced by their approximation functions. Components of the objective function are first and second order approximated and constraints are first order approximated. Conditions such that efficient solution of the approximate problem will remain efficient for initial problem and reciprocally are studied.

Numerical examples are developed to emphasize the importance of these conditions.

Downloads

Download data is not yet available.

References

D.I. Duca, A. Ratiu, Semi-infinite optimization problems and their first order approximations, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 11 (2013), pp. 87–94,

V. Chankong, Y. Haimes, Multiobjective Decision Making Theory and Methodology, North-Holland, (1983).

I. Chikalov, S. Hussain, M. Moshkov, Bi-criteria optimization of decision trees with applications to data analysis, European journal of Operational Research, vol. 266 (2018) no. 2, pp. 689–701, https://doi.org/10.1016/j.ejor.2017.10.021 DOI: https://doi.org/10.1016/j.ejor.2017.10.021

H. Konno, H. Yamazaki, Mean absolute deviation portfolio optimization model and its applications to Tokyo Stock Market, Management Science, 37 (1991) no.5, pp. 519–531, https://doi.org/10.1287/mnsc.37.5.519 DOI: https://doi.org/10.1287/mnsc.37.5.519

A. Mahalov, T.I. Luca, Minimax rule for energy optimization, Computers and Fluids, 151 (2017), pp. 35–45, https://doi.org/10.1016/j.compfluid.2016.08.014 DOI: https://doi.org/10.1016/j.compfluid.2016.08.014

A. Palacio, B. Adenso-Diaz, S. Lozano, S. Furio, Bi-criteria optimization model for locating maritime container depots: application to the port of Valencia, Networks and Spatial Economics, 16 (2016) no. 1, pp. 331–348, https://doi.org/10.1007/s11067-013-9205-7 DOI: https://doi.org/10.1007/s11067-013-9205-7

Downloads

Published

2018-12-31

How to Cite

Luca, T. I., & Duca, D. I. (2018). Approximations of objective function and constraints in bi-criteria optimization problems. J. Numer. Anal. Approx. Theory, 47(2), 167–176. https://doi.org/10.33993/jnaat472-1153

Issue

Vol. 47 No. 2 (2018)

Section

Articles

License

Copyright (c) 2019 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

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.