Existence of solutions and solving method of lexicographic problem of convex optimization with the linear criteria functions

Authors

  • N.V. Semenova V.M. Glushkov Institute of Cybernetics
  • M.M. Lomaha Uzhhorod National University
  • V.V. Semenov V.M. Glushkov Institute of Cybernetics

DOI:

https://doi.org/10.15407/dopovidi2020.12.019

Keywords:

cutting plane method, existence of solutions, lexicographic optimization, method of linearization, vector criterion

Abstract

Among vector problems, the lexicographic ones constitute a broad significant class of problems of optimization. Lexicographic ordering is applied to establish rules of subordination and priority. Hence, a lot of problems including the ones of complex system optimization, of stochastic programming under a risk, of the dynamic character, etc. may be presented in the form of lexicographic problems of optimization. We have revealed the conditions of existence of solutions of multicriteria of lexicographic optimization problems with an unbounded set of feasible solutions on the basis of applying the properties of a recession cone of a con vex feasible set, the cone which puts it in order lexicographically with respect to optimization criteria. The obtained conditions may be successfully used while developing algorithms for finding the optimal solutions of the mentioned problems of lexicographic optimization. A method of finding the optimal solutions of convex lexico graphic problems with the linear functions of criteria is built and grounded on the basis of ideas of the method of linearization and the Kelley cutting plane method.

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References

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Published

28.03.2024

How to Cite

Semenova, N. ., Lomaha, M. ., & Semenov, V. . (2024). Existence of solutions and solving method of lexicographic problem of convex optimization with the linear criteria functions . Reports of the National Academy of Sciences of Ukraine, (12), 19–27. https://doi.org/10.15407/dopovidi2020.12.019

Issue

Section

Information Science and Cybernetics

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