A Cutting Method with Approximation of a Constraint Region and an Epigraph for Solving Conditional Minimization Problems
- Authors: Shulgina O.N.1, Yarullin R.S.1, Zabotin I.Y.1
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Affiliations:
- Kazan (Volga region) Federal University
- Issue: Vol 39, No 6 (2018)
- Pages: 847-854
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202545
- DOI: https://doi.org/10.1134/S1995080218060197
- ID: 202545
Cite item
Abstract
We propose a method which belongs to a class of cutting methods for solving a convex programming problem. The developed method differs from traditional algorithms of the mentioned class by the following fact. This method uses approximation of the feasible set and the epigraph of the objective function simultaneously for the solving problem. In the method cutting planes are constructed by subgradients of the objective function and functions which define the constrained set. In this case while initial approximating sets are chosen as polyhedral sets, each iteration point is found by solving a linear programming problem independently of the type of functions which define the solving problem. Moreover, unlike most the cutting methods the proposed method is characterized by possibility of updating approximating sets due to dropping accumulating constraints.
About the authors
O. N. Shulgina
Kazan (Volga region) Federal University
Author for correspondence.
Email: ONShul@mail.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
R. S. Yarullin
Kazan (Volga region) Federal University
Email: ONShul@mail.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
I. Ya. Zabotin
Kazan (Volga region) Federal University
Email: ONShul@mail.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008