Informatics and Applications
2023, Volume 17, Issue 4, pp 17-22
PROCEDURE OF CONSTRUCTING A PARETO SET FOR DIFFERENTIABLE CRITERIA FUNCTIONS
Abstract
A ubiquitous computational procedure for the multicriteria optimization allows one to approximate the Pareto set under different requirements to the vector of particular efficiency criteria and the set of feasible solutions. In the paper, it is assumed that particular efficiency criteria are pseudoconcave in an open neighborhood of a compact convex set of feasible solutions which can be given by differentiable functional constraints. To build specific numerical methods for approximating the Pareto set, a rule for choosing the initial approximation and a rule for moving from the current reference solution to the next one are proposed.
[+] References (4)
- Rabinovich, Ya. I. 2017. Universal procedure for constructing a Pareto set. Comp. Math. Math. Phys. 57(1):45-63. doi:10.1134/S0965542517010122
- Bazaraa, M.S., and C.M. Shetty. 1979. Nonlinear programming: Theory and algorithms. New York, NY: Wiley. 872 p.
- Kuhn, H.W., and A.W. Tucker, eds. 1956. Linear inequalities and related systems. Annals of mathematics studies ser. Princeton, NJ:Princeton University Press. 322p
- Rabinovich, Ya.I. 2015. Numerical methods for esmating approximate solutions of multicriteria optimization problems. Dokl. Math. 91(3):384-386. doi: 10.1134/S1064562415030114. EDN: UFAQXF.
[+] About this article
Title
PROCEDURE OF CONSTRUCTING A PARETO SET FOR DIFFERENTIABLE CRITERIA FUNCTIONS
Journal
Informatics and Applications
2023, Volume 17, Issue 4, pp 17-22
Cover Date
2023-12-10
DOI
10.14357/19922264230403
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
multicriteria optimization; Pareto set; numerical methods of approximation; universal procedure
Authors
Ya. I. Rabinovich 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
|